What is the inverse of f(x)=-0.5(e^{2x}-1) ?

The inverse of f(x)=-0.5(e^{2x}-1) is (ln(-2x+1))/2

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inverse of f(x)=-0.5(e^{2x}-1)

inverse

f (x) = - 0.5 (e^{2 x} - 1)

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

Solution steps

y = - 0.5 (e^{2 x} - 1)

Replace

x

with

y

x = - 0.5 (e^{2 y} - 1)

Solve for

y, x = - 0.5 (e^{2 y} - 1)

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

f (x) = \frac{7}{x} - 2

4 (x - 7)^{2} + 3, x \leq 7

f (x) = \frac{3 x + 9}{4}

f (x) = (2 x - 5)^{3}

f (x) = 9 - 3 x

What is the inverse of f(x)=-0.5(e^{2x}-1) ?
The inverse of f(x)=-0.5(e^{2x}-1) is (ln(-2x+1))/2