Question

Let $f\left(x\right)=x^3$ be a function with domain {0, 1, 2, 3}. Then domain of $f^{-1}$ is
(a) {3, 2, 1, 0}
(b) {0, −1, −2, −3}
(c) {0, 1, 8, 27}
(d) {0, −1, −8, −27}

Answer 1

(c) {0, 1, 8, 27}

$$\begin{gathered} f\left(x\right)=x^3 \\ \text{Domain =}\left\{0,1,2,3\right\} \\ \text{Range =}\left\{0^3,1^3,2^3,3^3\right\}\text{=}\left\{0,1,8,27\right\} \\ \text{So,}f\text{=}\left\{\left(0,0\right),\left(1,1\right),\left(2,8\right),\left(3,27\right)\right\} \\ {\text{f}}^{-1}\text{=}\left\{\left(0,0\right),\left(1,1\right),\left(8,2\right),\left(27,3\right)\right\} \\ \text{Domain of}{f}^{-1}=\left\{0,1,8,27\right\} \end{gathered}$$