Question

If h(x) = f
`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:

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

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

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

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

cubing both sides ,we get

x+3 = g(x) +2

solving for g(x) ,we get

g(x) = x+1