Question

How do you find the compositions given `F(x)=x+4` and `g(x)=x^2`?

Answer 1

The composition of two functions is really just substituting one function as the x value of the other. See example below for detailed explanation.

Explanation:

Example 1: Find ƒ(g(2))

This means that what would be ƒ's y value when g's x value is 2. We find this by substituting 2 for x in g(x) and then putting the solution to that into ƒ(x).

ƒ(g(2)) = ƒ(`2^2`)

= ƒ(4) = 4 + 4

ƒ(g(2)) = 8

Example 2: Find g(ƒ(x))

= g(x + 4)
= `(x + 4)^2`
= `x^2` + 8x + 16

Hopefully you understand now