What is the inverse of f(x)=ln(-(x-5)/2)+1 ?

The inverse of f(x)=ln(-(x-5)/2)+1 is -2e^{x-1}+5

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inverse of f(x)=ln(-(x-5)/2)+1

inverse

f (x) = ln (- \frac{x - 5}{2}) + 1

- 2 e^{x - 1} + 5

Solution steps

y = ln (- \frac{x - 5}{2}) + 1

Replace

x

with

y

x = ln (- \frac{y - 5}{2}) + 1

Solve for

y, x = ln (- \frac{y - 5}{2}) + 1

- 2 e^{x - 1} + 5

f (x) = \frac{x ^{2} + 1}{x ^{2} + 5}

3 x^{2} + 4 x + 7

e^{- 12 x^{2}}

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

f (x) = x - 5, x \geq 5

What is the inverse of f(x)=ln(-(x-5)/2)+1 ?
The inverse of f(x)=ln(-(x-5)/2)+1 is -2e^{x-1}+5