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