What is the inverse of f(x)= 1/2 e^{x+3}-4 ?

The inverse of f(x)= 1/2 e^{x+3}-4 is ln(2x+8)-3

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inverse of f(x)= 1/2 e^{x+3}-4

inverse

f (x) = \frac{1}{2} e^{x + 3} - 4

ln (2 x + 8) - 3

Solution steps

y = \frac{1}{2} e^{x + 3} - 4

Replace

x

with

y

x = \frac{1}{2} e^{y + 3} - 4

Solve for

y, x = \frac{1}{2} e^{y + 3} - 4

ln (2 x + 8) - 3

What is the inverse of f(x)= 1/2 e^{x+3}-4 ?
The inverse of f(x)= 1/2 e^{x+3}-4 is ln(2x+8)-3