In Exercises 51–66, find c. (fog) (2)d. (go f) (2).f(x) = √x, g(x...

Question

In Exercises 51–66, find c. (fog) (2)d. (go f) (2).f(x) = √x, g(x) = x − 1

Accepted Answer

but this problem if you want to solve F of G of one and G F f of one for F of X equals to X to the one third and G F X equal X the third plus two. So let's write out our compositions. So we have F of G of X is equal to F on the outside and G F X on the inside. Furthermore R G F F of X that's equal to G on the outside half of X on the inside. I'm not gonna be right. Are you questions look here F of G of X. That is same as saying F of X cubed plus two. We plug in X two plus two for all of our X. S. And F. Same thing on the G where we'll plug in ex the one third for all of our exes All of our exes Let's work on at 1st You have f of x cubed plus two, that would be equal to X. Q plus two to the power of one thirds. So we want to simplify this. There's not really much we can do for simplification here Because everything is to the race of the power of 1/3. However, he thinks the power of one third is actually the cube. So I can regret this as the cube root FX III Plus two. Now it tells us we're at F of G of one so Rx is going to be equal to one. So we replace our X with one here at the cube group of X the third minus two. So once the third plus two. I'm sorry plus two minus two. And the Houston. Once the third plus two we get one plus two there Just the Cube of three. So our f. of G. of one is equal to the cubes of three. Now we'll do the same for our G. Of X. What we have G. X to the one third. That is going to be equal to X to the one third Raised the 3rd power plus two. Now we can actually simplify this because we have X. The 1/3 raise the third power. When you raise exponents to a power you multiply the exponents. This is the same as saying X to the one third times three plus two. Or in other words ex the one plus two or just X plus two. Now we can use our substitution. Well we have x equals one again. So We have g. of f. of one. It's equal to 1-plus 2 Which is just equal to three. The answer to our problem is answer. C. G of one is cooperative. Three. G. F. F. Of one is just three. Okay I hope that we solve the problem. Thank you for watching. Get back

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In Exercises 51–66, find c. (fog) (2)d. (go f) (2).f(x) = √x, g(x) = x − 1

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