If f(x) = (2x+5)/x, what is f^-1(x)?

1 Answer
Jun 27, 2017

f^-1(x)=\frac{5}{x-2}

Explanation:

f(x)=(2x+5)/x
x=f^-1((2x+5)/x)

Let y=(2x+5)/x
Now solve y=(2x+5)/x for y
yx=2x+5
yx-2x=5
x(y-2)=5
x=5/(y-2)

So,
x=f^-1((2x+5)/x)
5/(y-2)=f^-1(y)
And
,f^-1(x)=\frac{5}{x-2}