Question

Given that f(x)=2x+1,find g(x) if g(x)=2[f(x)]²-1

Answer 1

G(x)= 2[2x+1]^2-1. Where f(x) values is 2x+1
= 2[4x^2+4x+1]-1
=8x^2+8x+2-1
=8x^2+8x+1

Hope this helps!

Answer 2

$f(x)=2x+1\\\\g(x)=2\left[f(x)\right]^2-1\\\\g(x)=2\cdot(2x+1)^2-1=2\cdot[(2x)^2+2\cdot2x\cdot1+1^2\right]-1\\\\=2\cdot(4x^2+4x+1)-1=8x^2+8x+2-1=8x^2+8x+1$

Used:  $(a+b)^2=a^2+2ab+b^2$