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JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

Let

g(x)

be the inverse of

f(x)=\frac{2^{x+1}-2^{1-x}}{2^x+2^{-x}}

then

g(x)

be:

View answer and explanation

Correct option: A

\frac{1}{2} \log _2\left(\frac{2+x}{2-x}\right)

Option A is the correct answer. The inverse function

g(x)

is found by solving for

x

in terms of

y

and then swapping

x

and

y

, resulting in

g(x) = \frac{1}{2} \log _2\left(\frac{2+x}{2-x}\right)

.

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