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

Answer:

$x^2-6x+9$

Step-by-step 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!