5

21)Let f(x)-x 1and g() = 4 Find cach of the following:a) ( 0 g)(2)6) (g 0 f(2)c) ( o g)(1)(g 0 f1)g) (f . g)(*)h) (g 0 f)x)...

Question

21)Let f(x)-x 1and g() = 4 Find cach of the following:a) ( 0 g)(2)6) (g 0 f(2)c) ( o g)(1)(g 0 f1)g) (f . g)(*)h) (g 0 f)x)

21)Let f(x)-x 1and g() = 4 Find cach of the following: a) ( 0 g)(2) 6) (g 0 f(2) c) ( o g)(1) (g 0 f1) g) (f . g)(*) h) (g 0 f)x)



Answers

$$ \begin{array}{rl} {\text { Given that } f(-1)=4} & {g(-1)=-4} \\ {f(0)=5} & {g(0)=-3} \\ {f(2)=7} & {g(2)=-1} \\ {f(7)=1} & {g(7)=4} \end{array} $$ Find each function value. $$ (f \cdot g)(0) $$

I m times teaching. Well, san, it s zero times t times. We were given points in years of fun The equation of the points for graph f and graft teeth. The equation for graph was negative. Absolute value of X minus 27 M Fergie X minus three. So we're going to plug these equations into our equation, which is negative. Absolute value of X minus two plus seven chimes in a put apprentice. He's you put the equation for F and we're gonna do bad times X minus three times zero. This is one equation to sit in a creation. Okay. Okay, so now we're gonna prefer is gonna do zero times X, which is zero. There were times negative to it was 77. We know everything in this parentheses is gonna equal to zero because anything was acquired by several is zero. So we're just gonna put this here? You could know that everything is, and then after, never gonna do everything times would isn't disparate entities several times x zero times negative three, which is zero. So when you do zero time zero, you get Sarah. So I would answer is zero

Okay, So the important thing to know is that if you're given f of g of X and you're asked to find the derivative of this So I like this notation. Um, it's important to recognize that it's the derivative of the big thing times the derivative of the inside. So when you're given a problem like this, um, and they ask you to find f I forget exactly. Not a big fan of the notation, but half of g derivative when exit zero. That's basically saying, OK, take the derivative of G of zero times G, prime of zero. So now when you look at the given information, they tell you G prime of zero equals three. They tell you, Um, g of zero is zero. I just rewrite it this way. And now you need to recognize that they tell you f prime of zero is too. This Times three is still here. Um, so we're just left with two times. Three were just six. That's it.

This is this problem wants us to find the sum of f N G. I have to. So it really translated that this means we need to find Apple too. And And that g of two. Well, if you look above, we can see the f of two is just seven and g of twos. Negative one. So if we add this too, just get the value six. So f plus g of two or the sum of F N g of two is just gonna be the value six. Thank you.

So as you can see, I have a problem that we need to answer, you know, effortless G times two. Another way of saying that is F times two plus g times two. So we were given points. And first you need to find the equation for those points. And each points is for like, one of the points is for every one of the points is Fergie. So this these are the questions that I got for eight for them for ever got negative. Absolute value of X minus two plus seven in for Gee, I got X Ministry. I'm sure you does. How I got it. So this is the point for So these are the points that we're giving. And the closest graph I got to this point is the absolute value. There was no other graph where I could get all the points to be on the line. We have an ally, which is this one right here. So that's how I got my equation. I looked that and I figured out that it was a absolutely value. So I looked at this point right here, and from that point I decided how the graph moved and I just add It goes into the equation. So Fergie these air the point either the points Fergie. And as you can see, it's a straight line. It looked like a straight line, so I really know was a senior grand. So this is a question that I got for extra factory back. Now we need to do F times, too. We know that f is negative. Absolute value of X amount of stupid seven. So we're gonna do parentheses, four minutes, parentheses. Uh, we're going to parentheses. Negative. Absolute value of eggs minus two plus seven times to plus eggs, parentheses, eggs minus three times two. But this is also in different cities, so it looks okay. We're gonna solve the 1st 1 We're gonna do a different color we're doing We're gonna do two times everything that's in the parentheses. So two times we're gonna put the negative absolute value because they don't change to stay the same. We're gonna do two times X, which is to eggs and never going to two times two, which is forced to best negative for and we're gonna do, plus two times seven, which is 14 other days. Waas. I have a different definition. 202 times X, which is to eggs in two times three, which is six and at the negative. Negative. So we're gonna come my light terms. We can't combine this two x and two X because this two X is enough absolute value their way. Can't do anything to it. You have to live in an obsolete value. And that is so we're gonna just like everything That's an absolute value because we can't do anything to done. They're gonna add that to we have plus 14 and we have negative six. So these air, we could combine these light terms because they're not inside the parentheses in their part of the equation. So that's gonna be 14 minus six, which is eight, and we're gonna just put it, put two x on the side. So as you could see our final answer negative after the Valley of two X minus four plus eight plus two X equals F plus G times two


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