How do you find the inverse of #f(x) = 4 / (x+2)#?

1 Answer
May 8, 2017

Replace the original x with y and original y with x and solve for y.

Explanation:

We can find the inverse of any function by replacing the original function's x with y and y with x and solving.
For this function, #f(x)# is the same as y, so we can write this function as:
#y=4/(x+2)#
Now we flip the x and the y to get:
#x=4/(y+2)#
Now we solve for the new y:
#x(y+2)=4#
#y+2=4/x#
#y=4/x-2#
So our inverse function is: #f^(-1)(x)=4/x-2#