Let f(x)=x^5+2 x-3. Find (f^ -1 )^ (-3). - Vidyadip

Question

Let $f(x)=x^5+2 x-3$. Find $\left(f^{-1}\right)^{\prime}(-3)$.

✓

Answer

Given : $f(x)=x^5+2 x-3$
Diff. w. r.t.x we get,
$
f^{\prime}(x)=5 x^4+2
$
Note that $y=-3$ corresponds to $x=0$.
$
\begin{aligned}
\therefore \quad\left(f^{-1}\right)^{\prime}(-3) & =\frac{1}{f^{\prime}(0)} \\
& =\frac{1}{5(0)+2}=\frac{1}{2}
\end{aligned}
$

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