Question

Let f(x)=x+4 and g(x)=(x-2)^2.

Find u(x) so that f(g(u(x)))=4x^2 - 8x +8.

Answer 1

f o g(x)

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

By putting u(x)=2x, then
f o g o u(x)
=f(g(u(x)))
=(2x-2)^2+4
=4x²-8x+8