What is the inverse of f(x)=(2^x-2^{-x})/2 ?

The inverse of f(x)=(2^x-2^{-x})/2 is (ln(x+sqrt(x^2+1)))/(ln(2)),(ln(x-sqrt(x^2+1)))/(ln(2))

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inverse of f(x)=(2^x-2^{-x})/2

inverse

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

\frac{ln ( x + x ^{2} + 1 )}{ln ( 2 )}, \frac{ln ( x - x ^{2} + 1 )}{ln ( 2 )}

Solution steps

y = \frac{2 ^{x} - 2 ^{- x}}{2}

Replace

x

with

y

x = \frac{2 ^{y} - 2 ^{- y}}{2}

Solve for

y, x = \frac{2 ^{y} - 2 ^{- y}}{2}

\frac{ln ( x + x ^{2} + 1 )}{ln ( 2 )}, \frac{ln ( x - x ^{2} + 1 )}{ln ( 2 )}

What is the inverse of f(x)=(2^x-2^{-x})/2 ?
The inverse of f(x)=(2^x-2^{-x})/2 is (ln(x+sqrt(x^2+1)))/(ln(2)),(ln(x-sqrt(x^2+1)))/(ln(2))