Question

Which graph shows the inverse of the function f (x) = x^3?

Answer 1

`\text{The given function is f(x)=}x^3\text{.}`

`\text{Let f(x)=y.}`
`y=x^3`

Taking cube root on both sides, we get

`\sqrt[3]{y}=x`
`R\text{eplace x=}f^(-1)(y)\text{ since we taken y=f(x)}`

`f^(-1)(y)=\sqrt[3]{y}`
`\text{ Replace x=y, we get }f^(-1)(x)=\sqrt[3]{x}\text{ is the }inverse\text{ function of f(x)=}x^3\text{.}`

The given two graphs are parabolic graphs. Those are not the inverse of the given function.

`\text{The graph of the function is }f^(-1)(x)=\sqrt[3]{x}\text{ is}`

Hence this is the required graph.