If f(x)=x^5+2 x-3, then (f^ -1 )^ (-3)= ______. - Vidyadip

MCQ

If $f(x)=x^5+2 x-3$, then $\left(f^{-1}\right)^{\prime}(-3)=$ ______.

A
0
B
-3
C
$-\frac{1}{3}$
D
$\frac{1}{2}$

✓

Answer

$\frac{1}{2}$

$f(x)=x^5+2 x-3$
Differentiating w.r.t. $x$,
$
f^{\prime}(x)=5 x^4+2
$
If $y=-3$, then $x=0$
i.e. $y=-3$ corresponds to $x=0$
$
\begin{aligned}
\therefore\left(f^{-1}\right)^{\prime}(-3) & =\frac{1}{f^{\prime}(0)} \\
& =\frac{1}{5(0)+2}=\frac{1}{2}
\end{aligned}
$
Hence option (d)

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