In Exercises 51–66, find
a. (fog) (2)
b. (go f) (2)
f(x) = 4-x,...

Question

In Exercises 51–66, find 
a. (fog) (2)
b. (go f) (2) 
f(x) = 4-x, g(x) = 2x² +x+5

Accepted Answer

Solve F of G of zero and G of F zero. Where X equals four plus squared of X. G X equals X squared plus two. X plus two. Let's look at F of G of 0 1st. We can write this as FG zero. Like, so now our composition we're going to take what we have or our G X plug into the X for F of X equation. Other words, F f X squared plus two X plus two. That's the same thing as saying four plus square root of X squared plus two, X plus two. Instead. Now we want GF zero FMG of zero rather. So we're gonna plug in zero for X. Two squared plus two times zero plus two for their We get the square of two there. We can't simplify anymore. So we'll leave that as is. Now let's take a look at GFF of zero, of 0. We want G four plus squared of X. Well now substitute four plus square root of X everywhere. Where we have an X or plus squared of X squared plus two times four plus squared of X plus two. We can then simplify this at plus eight squared of X plus X. To expand our exponent there plus eight plus two squared of X. Us too. We're saying we can write this again simplifying once more as X Plus 10 squared of x plus 26. Now we plug in zero for X. We get zero plus 10 squared of zero plus 26. This just goes to 26. We now have both of our compositions. We can notice the answer to our problem turns out to be answer. B. 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) = 4-x, g(x) = 2x² +x+5

Key Concepts

Function Composition

Evaluating Functions

Quadratic Functions

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