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

The inverse of f(x)= 1/2 ln(x-1)+5 is e^{2x-10}+1

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

inverse

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

e^{2 x - 10} + 1

Solution steps

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

Replace

x

with

y

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

Solve for

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

e^{2 x - 10} + 1

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

f (x) = \frac{3 x + 1}{x + 2}

f (x) = ln (0.5)

f (x) = \frac{x}{2} + 2

y = 3 (x + 2)^{2} - 19

What is the inverse of f(x)= 1/2 ln(x-1)+5 ?
The inverse of f(x)= 1/2 ln(x-1)+5 is e^{2x-10}+1