Question

Given the following functions:

f(x)=x^2

g(x)=x−3

Find the composition of the two functions and show your process:

f(g(x))

Answer 1

`x^2-6x+9`

Explanation:

Say you have a function
`f(x)=x+1`. If you wanted to find f(3), you would replace the number in the parentheses, in this case 3, with x, to get
`f(3)=3+1=4.` When combining functions, you should do the same thing.

Here, we have
`f(x)=x^2.` We want to find f(g(x)). So, you should replace x in the function f(x) with the function g(x).
`g(x)=x-3.` So, f(g(x)) would equal
`(x-3)^2`, which equals
`x^2-6x+9`.

Hope this helps!