Question

Let f(x) = 4x2 + x + 1 and g(x) = x2 – 2. Find g(f(x)). Show each step of your work. Please don't just give the answer! Walk me through it. Thank you!

Answer 1

g(f(x)) means take f(x) and substitute it for x in g(x)

Answer 2

g(x) = x^2 - 2
g(f(x)) = f(x)^2 - 2 = (4x^2 + x + 1)^2 - 2

finish by expanding

Answer 3

actaully it was the other way around... anyhow =)

Answer 4

i'm confused now. what do you mean the other way around?

Answer 5

\(\bf f(x) ={\color{brown}{ 4x^2+x+1}}\qquad g(x)={\color{black}{ x^2-2}}
\\ \quad \\
g(\ {\color{brown}{ f(x)}}\ )=({\color{brown}{ f(x)}})^2-2\)

Answer 6

expand as Vocaloid suggested

Answer 7

okay... so g(f(x)) = (4x^2 + x + 1)^2 - 2. I'm probably way off, but 16x^4 + x^2 + 2 - 2.

Answer 8

just bear in mind that \(\bf (4x^2 + x + 1)^2 \implies (4x^2 + x + 1)(4x^2 + x + 1)\)

Answer 9

so was I right? I just had to take away the -2 at the end?

Answer 10

What are the steps I have to take? Maybe I can figure it out if you tell me the steps to get the answer. Thanks so much for helping me by the way.

Answer 11

not quite

(4x^2 + x + 1)^2 = (4x^2 + x + 1)*(4x^2 + x + 1)

use foil to expand

Answer 12

Okay. Foil = First, outer, inner, last?

Answer 13

yes

Answer 14

we also have a middle term in this case, x

Answer 15

a sec. pls

Answer 16

so it would be x squared in the middle