1 Answer

Arahant · Answer 1 · 2020-10-31T13:37:03+0000

Answer:

g(x)=x+1

The problem:

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

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

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

Explanation:

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

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

Replace
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) .

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