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

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

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inverse of (a^x-a^{-x})/2

inverse

\frac{a ^{x} - a ^{- x}}{2}

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

f (x) = \frac{x - 5}{2} + 1

f (x) = - 8 - 3 x

\frac{S}{S ^{2} + 4 S + 5}

f (x) = \frac{5 x}{3 + 5}

f (x) = (x + 3)^{2} - 1, x \geq - 3

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