In Exercises 89–90, express the given function h as a composition...

Question

In Exercises 89–90, express the given function h as a composition of two functions f and g so that h(x) = (f ○ g)(x). h(x) = (x^2 + 2x - 1)^4

Accepted Answer

Welcome back. I'm so glad you're here. We have got a composition function here. C. Of X equals the square root of X squared plus X minus 31. And we want to decompose it, we know that it is A. Of B of X. Which is the same thing as A of B of X. And we want to break it apart and figure out what our B of X and what are A. Of X. Ok well the B of X. This innermost one is what is being done to our X first. So if we were to write our square root of X squared plus 13 X minus 31 what's happening to that X first? Well, the first thing that's happening is that X is being squared and then adding 13 times the X and the minus 31. So that's our B of X. That's what's happening to it first. So B of X. Is X squared plus 13 X minus 31. And after we have taken care of that, what's happening to our function next next it's square root is being taken. So that's the second thing to happen. So are A. Of X Is taking the square root of X. And that's the same thing as X to the 1/ and now we can look at our answer choices and this matches with answer choice C. Well done. We'll catch you on the next one

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