f(x)=8/x-5. Find the symbolic representation for f^-1(x)

I don't know if this is right:
(x-5)y=8
x-5y=8
5y=8-x
5x/8x =f^-1(x)

To find the symbolic representation of the inverse function f^ -1(x), we need to interchange the roles of x and y in the original function f(x) and solve for y.

Given: f(x) = 8/(x-5)

Step 1: Replace f(x) with y.

y = 8/(x-5)

Step 2: Swap x and y.

x = 8/(y-5)

Step 3: Solve for y.

Multiply both sides of the equation by (y-5) to isolate y.

x(y-5) = 8

xy - 5x = 8

xy = 8 + 5x

Divide both sides of the equation by x to solve for y.

y = (8 + 5x)/x

Therefore, f^ -1(x) = (8 + 5x)/x is the symbolic representation of the inverse function.