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

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

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

inverse

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

ln (2 x + 4) - 1

Solution steps

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

Replace

x

with

y

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

Solve for

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

ln (2 x + 4) - 1

f (x) = x^{4} - 16 x^{3} + 22 x^{2}

\frac{x ^{2} + 5 x + 6}{x - 1}

f (x) = \frac{x + 1}{x - 4}

- \frac{5}{3}

x^{2} - x - 6

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