Question

If
`h(x) = (f`°
`g)(x)` and
`h(x) \sqrt[3]{x+3}`, find
`g(x)` if
`f(x) \sqrt[3]{x+2}`

Answer 1

g(x) = x + 1

Explanation:

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

h(x)=f(g(x)) (Equation 1)

`h(x)=\sqrt[3]{x+3}`

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

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

Replacing in the Equation 1:

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

Solving for g(x): Raising both sides to the power 3:

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

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