Question

Let f(x) = 3x2 – x 2 and g(x) = 5x2 – 1. Find f(g(x)). Show each step of your work.

Answer 1

easy, sub g(x) for x in f(x)

f(g(x))=3(g(x))^2-(g(x))^2

g(x)=5x^2-1
f(g(x))=3(5x^2-1)^2-(5x^2-1)^2=
3(25x^4-10x^2+1)-(25x^4-10x^2)=
2(25x^4-10x^2+1)=
50x^4-20x^2+2

f(g(x))=50x^4-20x^2+2