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Question Bank [2022] — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsQuestion Bank [2022]2 Marks
Question
Let $f(x) = x^5 + 2x – 3$ find $\left(f^{-1}\right)^{\prime}(-3)$
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Answer

$f(x)=x^5+2 x-3$
Differentiating w.r.t. $x$, we get
$f^{\prime}(x)=5 x^4+2$
At $y=-3, x=0$
$ \therefore\left(f^{-1}\right)^{\prime}(-3)=\frac{1}{f^{\prime}(0)}$
$=\frac{1}{5(0)^4+2}$
$=\frac{1}{2} $

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