5

The function is one-to-one. Find its inverse_((x) = X-7' X770A 0"'(x)= ZZ,*+0 0 B. 0"'(x) = 77"f Oc f-1(x) = 7x+7 X+0~7+Tx 0 D. fF1()=...

Question

The function is one-to-one. Find its inverse_((x) = X-7' X770A 0"'(x)= ZZ,*+0 0 B. 0"'(x) = 77"f Oc f-1(x) = 7x+7 X+0~7+Tx 0 D. fF1()= X#o

The function is one-to-one. Find its inverse_ ((x) = X-7' X77 0A 0"'(x)= ZZ,*+0 0 B. 0"'(x) = 77"f Oc f-1(x) = 7x+7 X+0 ~7+Tx 0 D. fF1()= X#o



Answers

For each function: a) Determine whether it is one-to-one. b) If the function is one-to-one, find a formula for the inverse. $$f(x)=7-x$$

This problem, we're giving the function. Each of X equals seven minus sex. The first goals problems is to determine if the function age is a 1 to 1 function. The easiest way to do that to do this, to graph the function on a cornet plane and then before the horizontal line test. So I graph each of X here as y equals seven minus x. My graphing calculator. We'll zoom out a better picture of the function here. We could see that is simply a linear function with slope minus one in Why Intercept of seven. If I draw any horizontal line straight across the graph here, I can see that any horizontal line drawn across the linear function Onley intersects the line once. Whether that be in the X axis and sell for Y equals 50 or y equals negative. 50. Always horizontal lines only cross H of X once. Why intersection? That is evidence that age of acts passes. The horizontal line test passes the Hlt or his until lying test. And that means the Interfax is indeed a one toe one function, which means that for any unique and put value, there is a unique output value that corresponds to it. In other words, different inputs have different outputs. It's now that we know that h of X is 1 to 1 that's find this inverse function. We're gonna say that. Why? People seven minus X swap Excellent y to get X equals seven minus y Sol from why I'll get X minus seven equals minus. Why and the positive Why is equal to minus acts plus seven. All right and funk interest function notation To get interest function inch The perception of Age of X is evil of minus acts plus seven on down the line. Go ahead, circle that. So we assume that the original function H of X, given the problem isn't 1 to 1. Function in the US is in rece function. H inverters of X is evil that negative acts plus seven

This problem, we had the function G of X equals quantity X plus seven cute to the third power. The first goal This problem is to identify whether or not the function g a fax is a 1 to 1 function. The easiest way to do this is to graft the function and then perform the horizontal line test. So I wanted a graphing calculator and type in the function of Y equal in quantity X Plus seven. Most wanted me to a certain power. We can see that this fun claims a cubic cubic crunching translated or shifted to the left by seven units. And when I zoom in a little bit on the function so now the goal is to perform the horizontal line test so we can see a no matter where I drama arbitrary horizontal line to be down here, down here along the X axis cell for above decks access no matter where I draw a horizontal line where horizontal lines only cross the function at one intersection point even minus seven, it looks like it might cross. You might hit at many points she keeps doing in infinitely you were seeing while it is a close call. The horizontal line only intersects the graph right once for any horizontal life. This tells us that for any unique X input, there is a totally unique why output associated with it or different inputs along the X axis always have different. Why outputs? So that means that this function G affects indeed passes horizontal line test, which means that this function is indeed a one, So one function. So since the one that one function we can now solved within first function G Did you say that why equals X plus seven here swap extra wide to get X is equal to why plus seven to third power. No need to solve for why I'll take the cube root of both sides to get the queue grew of X equal y plus seven. It's a track seven from both sides to get wind equal, the cube root of acts minus seven or inverse function notation. This would be in first function. G of X is equal to the cube root of X minus seven. There's are inverse function formula because we know that the original function G of X is indeed a 1 to 1 function as it passes the horizontal line test

So for this problem we are asked to write the inverse of this function and I'm going to do that by changing ffx into an X. And acts into a Y. And then I'm gonna try to get this fly by itself. So the first thing I would do is at sea. Yeah. And then I would multiply both sides by B. Now to get rid of that cubed, I would take the cube root of both sides. Mhm. Mhm. I'm gonna go ahead and distribute that be mhm. And then my final step would be to add A. Which would be outside of the square root and that would be the inverse of the original function.

This problem, we have the function f of X equals X cubed plus seven. The first goal This problem is to determine at this function f of X. Is it 1 to 1 function? The easiest way to do this is to graft function. It performed the horizontal line test. It's only graphing calculator and then type in the function y equals X cubed plus seven. You see, there's a cubic function over a wide range X values, and the goal here is to see free pass a horizontal line in New Orleans. Graph. How many times with a horizontal line intersect the graph? We'll zoom in a little bit, so we did better view of that. Nearly horizontal part of the graph there around y equals seven that has a horizontal line at Y equal. Six would intersect the graph once or y equals 7.5. Intercept the graph once over here. If I goto y equals seven, it's close. Unify, Pass a line. The horizontal line through y angle. Seven. It only passes through the graph right along the y axis. Looks like it might be hitting several points along here, but actually, it's one point you keep zooming in zooming, and you see that more clearly so you can see a numerary pass horizontal line. Every horizontal line only passes through the graph once betweens that for any given ex employee value, there's only one unique wine value associated to it. So in that case, our function F does. Indeed, past passes the horizontal line test, which means that F of X is indeed in one to one function because they want to want to find it's inverse function. All right, why equals execute Plus seven. We need to swap X and y to get X equals. Why cute plus seven insult for Why X minus seven equals y Cubed Day two Q Group on both sides to get why equals Q Group of X, minus seven. All right, this is inverse function notation to be. The inverse function of F of X is equal to the Q Groot of X minus seven. There's our formula with inverse function of F effects, and we also know again F of X is a 1 to 1 function because it past the horizontal line test


Similar Solved Questions

5 answers
Ir"CrulcAutr (c ul dcrirulict &7130,21.(b) Find W drrec heon (416.Arala ceun:(23.5umuler (emar14.
Ir" Crulc Autr (c ul dcrirulict & 713 0,21. (b) Find W drrec heon (416. Arala ceun: (23.5 umuler (e mar 14....
3 answers
Predict the major product(s} of the following reaction:2and 4 and$
Predict the major product(s} of the following reaction: 2and 4 and$...
5 answers
Ta-X'evaluale(#*y )dzdy4x047
Ta-X' evaluale (#*y )dzdy4x 047...
5 answers
Hwnis jointly the square of = and the cubc of = and interscly a5 the squzre root of w. Wcn Fidy wben < 2, and w=16,3 , = 3 ad @then72.9.Ptcvicw
Hwnis jointly the square of = and the cubc of = and interscly a5 the squzre root of w. Wcn Fidy wben < 2, and w=16, 3 , = 3 ad @ then 72.9. Ptcvicw...
5 answers
Find the derivative of h(x) = cos(sin(cosz)).
Find the derivative of h(x) = cos(sin(cosz))....
5 answers
Find Je . dv' for F _ 2yi (siny)j on the curve counterclockwise around the unit circle C starting at the point (1,0). Jc' &
Find Je . dv' for F _ 2yi (siny)j on the curve counterclockwise around the unit circle C starting at the point (1,0). Jc' &...
5 answers
The following data represent the afternoon high temperatures for 50 construction days during : year in St: Louis: 79 031 Construct frequency distribution for the data using five class intervals: b. Construct frequency distribution for the data using 10 class intervals Examine the results of (a) and (b) and comment on the usefulness of the frequency distribution in terms of temperature summarization capability:
The following data represent the afternoon high temperatures for 50 construction days during : year in St: Louis: 79 031 Construct frequency distribution for the data using five class intervals: b. Construct frequency distribution for the data using 10 class intervals Examine the results of (a) and...
5 answers
A company has 1 - and 2 -year bonds outstanding, each providing a coupon of $8 %$ per year payable annually. The yields on the bonds (expressed with continuous compounding) are $6.0 %$ and $6.6 %$, respectively. Risk-free rates are $4.5 %$ for all maturities. The recovery rate is $35 %$. Defaults can take place halfway through each year. Estimate the risk-neutral default rate each year.
A company has 1 - and 2 -year bonds outstanding, each providing a coupon of $8 %$ per year payable annually. The yields on the bonds (expressed with continuous compounding) are $6.0 %$ and $6.6 %$, respectively. Risk-free rates are $4.5 %$ for all maturities. The recovery rate is $35 %$. Defaults ca...
5 answers
A department store_ has four competitors: B,C,D. and E: Store A hires consultant to determina if the percentage of shoppers who prefer each of the five stores is the same A survey of 1125 randomly selected shoppers conducted and the results about wnich one of the stores shoppers prefer are below. Nuneer2 Echeerer [zp2ize 5)2 Erot 136938Find the critlcal value at ( 0.UuS.14.8602non of tnem4877~9,4877~14.8602
A department store_ has four competitors: B,C,D. and E: Store A hires consultant to determina if the percentage of shoppers who prefer each of the five stores is the same A survey of 1125 randomly selected shoppers conducted and the results about wnich one of the stores shoppers prefer are below. N...
5 answers
1 . f (x) 1 (1.04)* 10
1 . f (x) 1 (1.04)* 10...
5 answers
Let 𝑓(𝑥) = (1−2𝑥)/ (3+𝑥) . Find the derivative by definition(Difference-Quotient).
Let 𝑓(𝑥) = (1−2𝑥)/ (3+𝑥) . Find the derivative by definition (Difference-Quotient)....
5 answers
A stone is dropped off a cliff and hits the ground with a velocity of -120 ft/sec. What is the height of the cliff?
A stone is dropped off a cliff and hits the ground with a velocity of -120 ft/sec. What is the height of the cliff?...
5 answers
QuestionG0 pt 02 €95 DetailsIf n-11 I(x-bar)-34, and 5-5, find the margin of error at 98% confidence level Give your answer to two decimal placesSubmit QuestionJump to AnswerQuestion 5G0r pt 02 297 Details If n-30, E(x-bar)e40, Question Details and 5-9_ find the margin of error at 80% confidence levelGive your answer t0 tWo decimal placesSubmit QuestionJump to AnswerType here to search
Question G0 pt 02 €95 Details If n-11 I(x-bar)-34, and 5-5, find the margin of error at 98% confidence level Give your answer to two decimal places Submit Question Jump to Answer Question 5 G0r pt 02 297 Details If n-30, E(x-bar)e40, Question Details and 5-9_ find the margin of error at 80% co...
5 answers
3 3 8 j' 1 1 1 } # g 8 [ 3}8 L W 08 3 3 1 8 ! } 3 Ia 8 1 1 1 Ji 3 8 1
3 3 8 j' 1 1 1 } # g 8 [ 3}8 L W 08 3 3 1 8 ! } 3 Ia 8 1 1 1 Ji 3 8 1...
5 answers
A biochemist studying metabolism feeds her rats 3-[14C]-alanine (alanine labeled at the methyl group): Alanine can provide carbons for gluconeogenesis because of the reaction catalyzed by alanine aminotransferase:alanine + & ~ketoglutaratepyruvate + glutamateAfter sacrificing her rats she finds considerable 14C in the glucose. Where is the 14C located in the glucose?C5C6
A biochemist studying metabolism feeds her rats 3-[14C]-alanine (alanine labeled at the methyl group): Alanine can provide carbons for gluconeogenesis because of the reaction catalyzed by alanine aminotransferase: alanine + & ~ketoglutarate pyruvate + glutamate After sacrificing her rats she fin...
5 answers
QueSTion 5polnteSavedWhich of the following statement about the carbonyl group is NOT correct? A methyl group is less polar than carbonyl group: The oxygen in carbony] group form hydrogen bonds with water molecule: C-0 bonding strong polar covalent bond.Within molecule, the carbonyE group can be located next t0 an amino group_ The carbonyl group can donate an Ht and change the pH;
QueSTion 5 polnte Saved Which of the following statement about the carbonyl group is NOT correct? A methyl group is less polar than carbonyl group: The oxygen in carbony] group form hydrogen bonds with water molecule: C-0 bonding strong polar covalent bond. Within molecule, the carbonyE group can be...

-- 0.019041--