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Given the function f(z) f(a) f(a + h) = f(a + h) f(a)Az2 calculate the following values:...

Question

Given the function f(z) f(a) f(a + h) = f(a + h) f(a)Az2 calculate the following values:

Given the function f(z) f(a) f(a + h) = f(a + h) f(a) Az2 calculate the following values:



Answers

Calculate $f(a+h)$ and $[f(a+h)-$ $f(a)] / h$ for $h \neq 0$. $$f(x)=\frac{1}{x-2}$$

Hello. So here we have a function F of X is equal to two X squared minus three X. So for part A we are evaluating F. Of A plus H. So F of A plus H means go ahead and plug in A plus X. For X. So we get two times A plus H squared minus three times A plus H. Then we just um square out eight plus eight and 53. And we get this is going to be equal to a to a squared plus two eight squared plus four A H minus three times A minus three H. So there we have F. Of A plus H. And then party we have F. Of A plus H minus everyday. All divided by H. Whoa. That's crazy. Right so F B. We have here F F. Of A plus H minus F of a. All divided by H. Also explosion here. So therefore this is going to be equal to well just plugging in this here for X. In our function we get this is going to be equal to what A. To a squared plus a +28 squared Plus A four A. H minus three A minus three H. Uh Well we have minus to a squared plus three A. All divided awful divided by age which is going to be equal to a combine like terms two X squared plus four H minus three age. All divided by age which is gonna give us uh once the ages cancel out, we just get a two H. Plus uh for a minus three A. So there we have a different question of F. Of A plus H minus F. Of a. All divided by H. Take care.

It's question when you've been function, have every year. Next, Why zing you go, Jew Go! Signed up a new minus Do ecstasy off. Why breast See? So the 1st 1 to computer half under 01234 Get any coaching course NYSE Oh, my Enough! Uh, June times one times three on. But you're plus three And then we get called you one Mine us. This will be the six out of five sewing and ico June minus one out of five. The next one to find the informed of Hae Ju zero minus 1/2 organic Because I'm the I minus, they will have a Jew times Teoh, Disappointment Your writing. By the zero last one, you get equal to minus one and then, uh minus the far and then we get included a minus five

All right, so they give us a already composed function, and they wanted to find an F N G that would compose together F g. We will get one plus x squared, all raised to the third power. So again, this reads f of G, so she's going to be plugged into F. So I think the easiest part is to start with something that we can plug into function to get something cute. In this case, I think one plus X squared is the easiest choice for G. And then f of X will be X cubed weaken double check f of G, and that's going to be one plus X squared than Q because that's plugging G and two F.

And this problem we have been given a function H of X and it is said that this is equal to two X cubed plus X square plus one. Hold to the power five. We need to determine two functions Fn Diesels that H is equal to the composition. Now let us use inspection too. Consider the two functions F of X and DX. Let us consider F of X to be the inner function. So F of X will be to execute plus X square plus one. And let us consider G H to be the outer function. So this to the power five. So G of X is equal to X to the power five. Now let us verify whether it is really equal to decomposition it or not. So let us determine the composition F of X, which by the definition of the composition of two functions is equal to G of F of X. That this will be equal to G of two X Q plus X square plus one. Now we can obtain the of this expression by replacing X by this expression and the expression for G of X. So what we end up with is two X. Q plus X square plus one hole to the power five. And this is the expression for each of X. Hence we can see the decomposition F of X is equal to H of X for all X. And hence each is equal to G. Composition F. That's the required functions will be F of X is equal to two X cubed plus expert plus one, and D O X is equal to actually power five.


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