please help me with this

Question

Use abs(x) for |x||x|.

Given that f(x)=|x|f(x)=|x| and g(x)=6x−3g(x)=6x-3, calculate

(a) f∘g(x)f∘g(x)=   

(b) g∘f(x)g∘f(x)=   

(c) f∘f(x)f∘f(x)=   

(d) g∘g(x)g∘g(x)=

Answer 1

Hi Morgen!

Assuming that each of those functions were accidentally duplicated, we're just looking at some standard composite functions.

A little review on functions: When you solve some random function h(x), the () allow you to replace x in the equation with any number or variable you'd like. For instance, if h(x) = x + 5, then h(3) = 3 + 5 = 8. It can be helpful to write it out as h(3) = (3) + 5 so that you know where you need to insert your input.

For composite functions, instead we replace "x" with some other function. The " ∘" symbol just means: f∘g(x) = f(g(x)). In other words, all you have to do is plug in the function g(x) where the x shows up in the function f(x).

I'll go through the first one, and we'll see if that clears things up for you enough to do the rest.

a) f∘g(x) = ?

Given: f(x) = |x|, g(x) = 6x - 3

Since f∘g(x) = f(g(x)), we just plug in g(x) anywhere that x shows up in the function f(x).

f(x) = |x|, so f(g(x)) = |g(x)| = |6x - 3| See how we just plug the second function into the first?

Our final result is: f∘g(x) = |6x - 3|

Hope this helps!