In Exercises 51–66, find
a. (fog) (x)
b. (go f) (x)
f(x) = x²+2...

Question

In Exercises 51–66, find 
a. (fog) (x)
b. (go f) (x) 
f(x) = x²+2, g(x) = x² – 2

Accepted Answer

solve F m G of X and G f f of X. Where f X equals x squared minus X and G X equals four minus X. This function is a composition of functions both of them are so F of G of X is the same thing as saying F G X with the X on the inside of parentheses. Same thing for G X. Just like this. So let's look at FMGMX 1st. This means that we're going to take what we have for G X and plug it into the X and F of X. Why did you write this? We can f Have four -X. So F four minus X instead of putting X, we're gonna put four minus X everywhere. So four minus X squared -4 -1. Now we can simplify this. No simplifies. Look here we have four minus X squared. This is same as saying four minus X times four minus x. Which were the multiply one Supplier Ford's first to give us our foreign negative X. To give us negative four X native except for to give us another negative four X. And finally Native X times X. To give us plus X squared. This should be our negative here to get negative four and positive X. Now we can simplify this. Gonna put my X squared first just for orders sake. Then we combine our terms, we have negative four X minus four X plus X negative four minus four is negative eight plus one is negative seven X. And then we have 16 -4 which gives us plus 12. So F G of X. Is X squared minus seven X plus 12. Now it's like a g F F. Of X. G of F of X. That's the same. The same G X squared minus x. Inside the parentheses simplify this. We will get four minus x squared minus X. Should we are negative? You get four minus X squared plus X. Finally we can reorganize with X square in the front. Now you have X squared plus X plus four. So we now have two equations X squared minus seven X plus 12. And we have negative X squared minus X plus four. The answer to our problem? It's answer. C. Okay I hope that you solve the problem. Thank you for watching. Goodbye.

In Exercises 51–66, find a. (fog) (x) b. (go f) (x) f(x) = x²+2, g(x) = x² – 2

Key Concepts

Function Composition

Quadratic Functions

Evaluating Functions

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