Answer:
g(x) = x + 1
Step-by-step explanation:
h(x)=(f o g)(x)
h(x)=f(g(x)) (Equation 1)
[tex]h(x)=\sqrt[3]{x+3}[/tex]
[tex]f(x)=\sqrt[3]{x+2}[/tex]
[tex]f(g(x))=\sqrt[3]{g(x)+2}[/tex]
Replacing in the Equation 1:
[tex]\sqrt[3]{x+3}=\sqrt[3]{g(x)+2}[/tex]
Solving for g(x): Raising both sides to the power 3:
[tex](\sqrt[3]{x+3})^{3}=(\sqrt[3]{g(x)+2})^{3}[/tex]
x+3=g(x)+2
Subtracting 2 from both sides of the equation:
x+3-2=g(x)+2-2
x+1=g(x)
g(x)=x+1
