Question

Identify the inside function, u = g(x),and the outside function, y = f(u).
y = (x^2 − 2x + 4)^2
Can someone help me figure out (u, y) = (g(x), f(u)) =? I have no instruction on this type of problem at all, so I need walked through it ALL. Please help?!!!!?

Answer 1

hmm
well.... looks to me like a case of y = f( g(x) )

Answer 2

\(\bf y=f({\color{brown}{ u}})\qquad {\color{brown}{ u}}=g(x)\quad thus\quad y=f({\color{brown}{ u}}) \iff y = f(\quad g(x)\quad )\)

Answer 3

so... what do you think?

Answer 4

well the usual suspect will be that f(x) is the one with the exponent
and the g(x) is the base

so \(\large \bf y ={\color{blue}{ f(\quad {\color{brown}{ g(x)}}\quad )}}= {\color{blue}{ ({\color{brown}{ x^2 - 2x + 4}})^2}}\) any ideas?

Answer 5

soo it would be: x^2-2x+4, u^2?

Answer 6

yeap g(x) and f(x) respectively

Answer 7

\(\bf f(u)=u^2\qquad {\color{brown}{ g(x)}}=x^2 - 2x + 4
\\ \quad \\
f(\quad g(x)\quad )={\color{brown}{ g(x)}}^2\to ({\color{brown}{ x^2 - 2x + 4)}})^2\leftarrow y\)

Answer 8

Thank you!

Answer 9

yw