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 for f^-1(x), we need to find the inverse of the function f(x)=8/(x-5).
To find the inverse, we'll start by swapping the x and y variables and solve for y.
So, we have:
x = 8/(y-5)
Now, let's solve for y.
Multiply both sides of the equation by (y-5) to get rid of the denominator:
x(y-5) = 8
Expand the equation:
xy - 5x = 8
Rearrange the equation to isolate y:
xy = 8 + 5x
Divide both sides by x:
y = (8 + 5x)/x
The expression (8 + 5x)/x represents the inverse function f^-1(x).