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

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

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

inverse

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

- 2 e^{x} + e^{2 x} + 3

Solution steps

y = ln (1 - x - 2)

Replace

x

with

y

x = ln (1 - y - 2)

Solve for

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

- 2 e^{x} + e^{2 x} + 3

f (x) = 25 x + 10

g (x) = - 2 (x + 3)^{3}

f (x) = 3 (x + 4)^{2} - 2, x \leq - 4

f (x) = \frac{2}{3} x - \frac{4}{3}

f (x) = \frac{x}{1 - x}

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