What is the inverse of f(x)=2^{x-1}-2^{-x-1} ?

The inverse of f(x)=2^{x-1}-2^{-x-1} 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-1}-2^{-x-1}

inverse

f (x) = 2^{x - 1} - 2^{- x - 1}

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

Solution steps

y = 2^{x - 1} - 2^{- x - 1}

Replace

x

with

y

x = 2^{y - 1} - 2^{- y - 1}

Solve for

y, x = 2^{y - 1} - 2^{- y - 1}

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

(2 x - 5)^{2}

6 x + 4

f (x) = - 3 x - 15 + 14

h (x) = \frac{3}{4} x + \frac{2}{7}

3 2 x + 4

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