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

Question

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

Accepted Answer

Solve F. Of G. Of negative one and G of F of negative one. Where F. Of X. Is equal to X squared minus X. G X. Is equal to four minus X. Let's look at F. Of G of negative one first. We can rewrite this like so now we want to find what our F. Of G. Of X is. In other words we're going to take what we have for the G F. X. And plug it into the X for F. Of X. So read this as F four minus X. Which time we can put into our exponent here four minus X squared. And we'll put it into the X. As well minus four minus X. Like so we can now expand this We will get 16 minus eight X plus X squared minus four plus X. This simplifies the X squared plus. I'm sorry not plus but a minus seven x plus 12. Now I plug in our -1. Neither one squared by the seven times. Either one plus 12. We have one plus seven, That's 12. Which gives us 20. Now do the same for Gs Athletics. Do you have F of X? People have T of X squared minus X. We should give it a rewrite S four minus X squared minus X. Like. So simplifying we get four minus X squared plus X. We can now plug in our -1. Four minus negative one squared minus one is four -1 -1 or two. We now have both of our compositions as 20 and two. This makes the answer to our problem answer. C. Okay, I hope to help you solve the problem. Thank you for watching. Goodbye.

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

Key Concepts

Function Composition

Evaluating Functions

Quadratic Functions

Watch next