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

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

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

inverse

f (x) = 2 + ln (x - 1)

e^{x^{2} - 4 x + 4} + 1

Solution steps

y = 2 + ln (x - 1)

Replace

x

with

y

x = 2 + ln (y - 1)

Solve for

y, x = 2 + ln (y - 1)

e^{x^{2} - 4 x + 4} + 1

f (x) = 300 \cdot 4^{x}

f (x) = ln (ln (ln (x)))

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

f (x) = 3 x^{3} - 9

f (x) = lo g_{5} (x) + lo g_{5} (7)

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