What is the inverse of f(x)=3+sqrt(1/(x-1)) ?

The inverse of f(x)=3+sqrt(1/(x-1)) is (x^2-6x+10)/(x^2-6x+9)

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inverse of f(x)=3+sqrt(1/(x-1))

inverse

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

\frac{x ^{2} - 6 x + 10}{x ^{2} - 6 x + 9}

Solution steps

y = 3 + \frac{1}{x - 1}

Replace

x

with

y

x = 3 + \frac{1}{y - 1}

Solve for

y, x = 3 + \frac{1}{y - 1}

\frac{x ^{2} - 6 x + 10}{x ^{2} - 6 x + 9}

f (x) = 6^{x} + 5

y = - x^{2} + 10

g (x) = 3 x + 4

\frac{3}{x ^{2} + 1}

What is the inverse of f(x)=3+sqrt(1/(x-1)) ?
The inverse of f(x)=3+sqrt(1/(x-1)) is (x^2-6x+10)/(x^2-6x+9)