Question

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

Answer 1

Answer:

$g(x)=x+1$

The problem:

Find $g(x)$ if $h(x)=(f \circ g)(x)$,

$h(x)=\sqrt[3]{x+3}$, and

$f(x)=\sqrt[3]{x+2}$.

Step-by-step explanation:

$h(x)=(f \circ g)(x)$

$h(x)=f(g(x))$

Replace $x$ in $f(x)=\sqrt[3]{x+2}$ with $g(x)$ since we are asked to find $f(g(x))$:

$\sqrt[3]{x+3}=\sqrt[3]{g(x)+2}$

$\sqrt[3]{x+1+2}=\sqrt[3]{g(x)+2}$

This implies that $x+1=g(x)$

Let's check:

$(f \circ g)(x)$

$f(g(x))$

$f(x+1)$

$\sqrt[3]{(x+1)+2}$

$\sqrt[3]{x+1+2}$

$\sqrt[3]{x+3}$  which is the required result for $h(x)$.