Question

F(x)= 2x^2 +1
g(x)= 7x-9
(f o f)(-2)

Answer 1

This is just a notation thing, once you understand it this becomes easy.

Let's say h(x) = 2x. In this case we know things like h(2) is 2(2) which is 4. Note that we can also input other variables. In fact this is the very manner in which defined the function. If h(x) = 2x than h(y) = 2y.

Now we try defining a variable, let's use u as something. let's say u = 32x+7. We already know h(u) = 2u. Now substitute in u, and we find h(u) = 2(32x+7). If we rewrite u in function notation we can write this as h(u(x)) = 2(32x+7). Basically what we've done here is we put one function inside another function.

This is the notation part. h(u(x)) can be rewritten as (h o u)(x).

And that's all there is to it!

Answer 2

163

Explanation:

"(f o f)(-2)" is a command asking you to use function f (evaluated at x= -2) as the input to another case of function f. Here are some examples:

f(x) = 2x^2 + 1.

We can evaluate this for several different inputs as examples of evaluating a function:

f(0) = 2(0)^2 + 1 = 1

f(-5) = 2(-5)^2 + 1 = 50+1

f(g) = 2(g)^2 + 1 = 2g + 1

f(f) = 2(f)^2 + 1 = 2f^2 + 1 Note: this is called a "composite function."

This leads up to the problem we're working on: Evaluate f(f(x)) for x = -2:

f(-2) = 2(-2)^2 + 1 = 8 + 1 = 9

Now use this result, 9, as the input to f(x): f( f(-2) ) = f( 9 ) = 2(9)^2 + 1 = 162 + 1 = 163.