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.