I still need help with finding the inverese of one to functions.

Find the inverese of the one to one function.

16. f(x)= 4/(5x-1)
This is what I've done so far.

y=4/(5x-1)
x= 4/(5y-1)
(5y-1)x= 4(5y-1)

Then I am not too sure what to do next.

The last line is wrong:

(5y-1)x= 4
5yx= 4+x
y= (x+4)/5x

y=(x+4)/5x, doesnt match up with what I am suppose to get.

I am suppose to get:
a. f^-1(x)=4/(5y) +1/5, b. f^-1(x)=4/(5x) +1/(5), c. f^-1(x)= -1/(5) -4/(5x), or d. f^-1(x)=5x-1/(4)

y=(x+4)/5x= 1/5 +4/5x

x=1/5+4/5y

To find the inverse of a function, you need to switch the positions of x and y and solve for y.

Starting with your equation:

(5y-1)x = 4(5y-1)

Let's solve this equation step by step:

1. Distribute the 4 on the right-hand side:
5yx - x = 20y - 4

2. Move all terms involving y to one side:
5yx - 20y = x - 4

3. Factor out y on the left-hand side:
y(5x - 20) = x - 4

4. Divide both sides by (5x - 20):
y = (x - 4) / (5x - 20)

So, the inverse function of f(x) = 4/(5x-1) is given by:

f^(-1)(x) = (x - 4) / (5x - 20)

This is the equation that represents the inverse of the original function.