Another composition question

[jinx24]

"Let f(x) = 1 - 2x^2 and g(x) = x + 1"

Find (f o f)(x)

1 - 2(1 - 2x^2)^2

I hit a snag when I foiled it out.

= 1 - 4x^2 - 2x^4 Not sure if this is right

When I do the last part of the foil (-2x^2)(-2x^2) do I include the negative or not. I know that when you multiply with exponents, if the base is the same, you just add the exponents and keep the base. So, I am not sure if the negative is part of the base.

Thank you!

ETA: Just thought of this (A - B)^2 = A^2 - 2AB + B^2
So I suppose the negative is not included. Let me know if I am wrong.

 

[Unco]

f(g(x)) = f(x+1) = 1 - 2(x + 1)^2

There's no obligation to expand, but for your question: (-2x^2)(-2x^2) = +4x^4 (and exponents are not being multiplied).

 

[jinx24]

Hi Unco! Thank you, once again for helping me!

The question was actually (f o f), not (f o g). I couldn't tell if you saw that or if you were just giving me a similar example.

You said that I don't need to expand. How do I know when to expand and when not to? Or does that even matter?

Thank you.
Jenny

ps...I see what you mean with the exponents.

 

[Unco]

You're absolutely correct.

Expanding here will simplify a little bit.