What is the inverse of f(x)=sqrt((7x+6)/(x-5)) ?

The inverse of f(x)=sqrt((7x+6)/(x-5)) is (6+5x^2)/(x^2-7)

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inverse of f(x)=sqrt((7x+6)/(x-5))

inverse

f (x) = \frac{7 x + 6}{x - 5}

\frac{6 + 5 x ^{2}}{x ^{2} - 7}

Solution steps

y = \frac{7 x + 6}{x - 5}

Replace

x

with

y

x = \frac{7 y + 6}{y - 5}

Solve for

y, x = \frac{7 y + 6}{y - 5}

\frac{6 + 5 x ^{2}}{x ^{2} - 7}

What is the inverse of f(x)=sqrt((7x+6)/(x-5)) ?
The inverse of f(x)=sqrt((7x+6)/(x-5)) is (6+5x^2)/(x^2-7)