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  • <img alt="\mathrm{\text { If } g \text { is the inverse function of } f \text { and } f^{\prime}(x)=\sin x \text {, then } g^{\prime}(x) \text { is equal to }}" src="https://entrancecorner.oncodeco

\mathrm{\text { If } g \text { is the inverse function of } f \text { and } f^{\prime}(x)=\sin x \text {, then } g^{\prime}(x) \text { is equal to }}

Option: 1

sin (g(x))
 


Option: 2

cosec(g(x))
 


Option: 3

tan(g(x))
 


Option: 4

none of these.


Answers (1)

best_answer

Given g(x)=f^{-1}(x)

So, x=f[g(x)]

Differentiating w. r. t. x,

We get 1=f^{\prime}[g(x)] \cdot g^{\prime}(x)

\begin{aligned} & \text { Hence } g^{\prime}(x)=\frac{1}{f^{\prime}(g(x))}=\frac{1}{\sin (g(x))} \\ & \Rightarrow g^{\prime}(x)=\operatorname{cosec}(g(x)) . \end{aligned}

Posted by

Shailly goel

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