Let f(x)

Question:

Let $f(x)=x^{3}$ 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) $\{0,-1,-8,-27\}$

Solution:

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

$f(x)$

$=x^{3}$

Domain $=$

$\{0,1,2,3\}$

Range $=$

$\left\{0^{3}, 1^{3},\right.$,

$2^{3}, 3^{3}$

\}$=$

$\{0,1,8,$,

$27\}$

So, $f$

$=$

$\{(0,0),$,

$(1,1)$,

$(2,8)$,

$(3,27)\}$

$\mathrm{f}^{-1}=$

$\{(0,0),$,

$(1,1)$,

$(8,2)$,

$(27,3)\}$

Domain of $f^{-1}=\{0,1,8,27\}$

Leave a comment

Close
faculty

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now