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

The inverse of f(x)= 1/2 e^{2x-1}-2 is (ln(2x+4)+1)/2

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

inverse

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

\frac{ln ( 2 x + 4 ) + 1}{2}

Solution steps

y = \frac{1}{2} e^{2 x - 1} - 2

Replace

x

with

y

x = \frac{1}{2} e^{2 y - 1} - 2

Solve for

y, x = \frac{1}{2} e^{2 y - 1} - 2

\frac{ln ( 2 x + 4 ) + 1}{2}

f (x) = 3 (x^{2} + 1)

f (x) = - x^{6} + 5

f (x) = 3 x - 1 + 2

y = \frac{( 2 x - 5 )}{3 x}

f (x) = 3 x - 1 + 5

What is the inverse of f(x)= 1/2 e^{2x-1}-2 ?
The inverse of f(x)= 1/2 e^{2x-1}-2 is (ln(2x+4)+1)/2