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

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

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

inverse

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

e^{2 x + 1} \cdot 2

Solution steps

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

Replace

x

with

y

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

Solve for

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

e^{2 x + 1} \cdot 2

y = (x - 1)^{2} + 3

2 x^{3} - 2

y = (x - 1)^{2} + 5

2 x^{3} - 9

- x^{2} + 25

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