Question

Let f(x) = 3x^2 – x + 2 and g(x) = 5x^2 – 1. Find f(g(x)). Show each step of your work.

Answer 1

@peachpi

Answer 2

\( g(x) = 5x^2 – 1\)
\(f(x) = 3x^2 – x + 2\)
\(f[g(x)] = f(5x^2 – 1) = 3[5x^2 – 1]^2 – [5x^2 – 1] + 2 \)

this what you meant??

hope it helps :p

Answer 3

\(\bf f(x)=3x^2-x+2\qquad g(x)={\color{brown}{ 5x^2-1 }}
\\ \quad \\
f(\ {\color{brown}{ g(x)}}\ )=3x({\color{brown}{ g(x)}})^2-({\color{brown}{ g(x)}})+2
\\ \quad \\
f(\ {\color{brown}{ g(x)}}\ )=3x({\color{brown}{ 5x^2-1}})^2-({\color{brown}{ 5x^2-1}})+2\)

Answer 4

so do you sole this?

Answer 5

just distribute and simplify, sure

Answer 6

25x^2-3x^2+25x^2-3^2+2?

Answer 7

hmm, notice, the 1st term has an squared binomial
you need to expand that one first

Answer 8

\(\bf f(\ {\color{brown}{ g(x)}}\ )=3x({\color{brown}{ 5x^2-1}})^2-({\color{brown}{ 5x^2-1}})+2
\\ \quad \\
f(g(x))=3x({\color{brown}{ 25x^4-10x^2+1}})-5x^2+1+2\)

Answer 9

why x4

Answer 10

@jdoe0001

Answer 11

\(\bf (5x^2-1)^2\iff (5x^2-1)(5x^2-1)\implies (25x^4-10x^2+1)\)

Answer 12

you can FOIL if you want

Answer 13

ojok