What is the inverse of f(x)= 1/2 ln(2x-1) ?

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

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inverse of f(x)= 1/2 ln(2x-1)

inverse

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

\frac{e ^{2 x} + 1}{2}

Solution steps

y = \frac{1}{2} ln (2 x - 1)

Replace

x

with

y

x = \frac{1}{2} ln (2 y - 1)

Solve for

y, x = \frac{1}{2} ln (2 y - 1)

\frac{e ^{2 x} + 1}{2}

(- 7, 8), (- 1, 1)

y = x^{2} - 4

\frac{1}{x - 1}

(3, 5), (- 7, - 7)

f (x) = (x + 1)^{5} - 1

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