Search any question & find its solution
Question:
Answered & Verified by Expert
If $f: R \rightarrow R$ is defined by $f(x)=x^{3}$, then $f^{-1}(8)=$
Options:
Solution:
1060 Upvotes
Verified Answer
The correct answer is:
$\{2\}$
Let $f^{-1}(8)=x$
$$
\begin{array}{lrlrl}
& \Rightarrow & & f(x) & =8 \\
\Rightarrow & & x^{3} & =8 \\
\Rightarrow & & x & =2 \\
& \therefore & & f^{-1}(8) & =\{2\}
\end{array}
$$
$$
\Rightarrow \quad x=2 \quad[\because x \in R]
$$
$$
\begin{array}{lrlrl}
& \Rightarrow & & f(x) & =8 \\
\Rightarrow & & x^{3} & =8 \\
\Rightarrow & & x & =2 \\
& \therefore & & f^{-1}(8) & =\{2\}
\end{array}
$$
$$
\Rightarrow \quad x=2 \quad[\because x \in R]
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.