Answer
$f^{-1}(x)=\dfrac{7x+5}{x-2}$
Work Step by Step
$f(x)=\dfrac{2x+5}{x-7}$
Rewrite this expression as $y=\dfrac{2x+5}{x-7}$ and solve for $x$:
$y=\dfrac{2x+5}{x-7}$
Take $x-7$ to multiply the left side:
$y(x-7)=2x+5$
$xy-7y=2x+5$
Take $-7y$ to the right side and $2x$ to the left side:
$xy-2x=7y+5$
Take out common factor $x$ from the left side:
$x(y-2)=7y+5$
Take $y-2$ to divide the right side:
$x=\dfrac{7y+5}{y-2}$
Interchange $x$ and $y$:
$y=\dfrac{7x+5}{x-2}$
The inverse of the initial function is $f^{-1}(x)=\dfrac{7x+5}{x-2}$
