Question: Given that f(x)=x^2. F(2x-1)=g(2x-5). Prove that g(x)=x^2+8x+16. ?
Given: f(x) = x^2
And: f(2x-1) = g(2x-5)
From the given, g(2x-5) = (2x-1)^2
g(2x-5) = {(2x-5) + 4)}^2 = (2x-5)^2 + 8(2x-5) + 16
i.e. g(u) = u^2 + 8u + 16
or, g(x) = x^2 + 8x + 16