Question

If h(x)=(fog)(x) and h(x)=^3√x+3, find g(x) if f(x)=^3√x+2.

Answer 1

Problem attached below. Please help and explain. Thank you to those who help!

Answer 2

\(\large f(x) = \sqrt[3]{x+2}\)
\(\large h(x) = (f \circ g)(x) = f(g(x)) = \sqrt[3]{x+3}\)

Given \(\large f(x) = \sqrt[3]{x+2}\)

\(\large f(?) = \sqrt[3]{x+3}\)

Answer 3

What should x in f(x) be replaced with to end up with \(\large \sqrt[3]{x+3}\) ?

Answer 4

\(\large f(x) = \sqrt[3]{x+2}\)
\(\large f(g(x)) = \sqrt[3]{g(x)+2} = \sqrt[3]{x+3} \)
\(\large g(x) + 2 = x + 3 \)
\(\large g(x) = x + 3 - 2 \)
\(\large g(x) = x + 1 \)