Find the F o F(x) and G o G(x)

Question

Answer 1

Hi Jack,

This can look confusing at first, so let's start with a simpler example.

If I asked you to find F(2), you would go ahead and substitute a 2 everywhere you see an x in F(x).

So, F(2) = 2^2-9(2)

= 4-18

= -14

Using that same idea, when asked to find F o F(x), another way to picture it is to write it as F(F(x)). Since F(x)=x^2-9x, what you want to do is find F(x^2-9x). Go ahead and substitute x^2-9x everywhere you see x in F(x).

This leads to F(F(x)) = F(x^2-9x)

=(x^2-9x)^2 - 9(x^2-9x)

Another way to write this is (x^2-9x)(x^2-9x)-9(x^2-9x)

If you know how to expand this, multiply everything out, and reach out again if you need more assistance. This should get you started.

All the best!

Natalie