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.