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

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

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inverse of f(x)=ln(2+e^{x-3})

inverse

f (x) = ln (2 + e^{x - 3})

ln (e^{x} - 2) + 3

Solution steps

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

Replace

x

with

y

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

Solve for

y, x = ln (2 + e^{y - 3})

ln (e^{x} - 2) + 3

f (x) = 8 x^{7} - 5

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

f (x) = 2 (x + 4)^{2} - 5

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

f (x) = - x^{2} - 8 x - 8

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