Question

Determine whether the following function is a one-to-one function,and if the function is a one-to-one, find a formula for the inverse.
F(x)=5/(x+3)

Answer 1

Inverse:
step 1. switch the x and y variables

y = 5/(x+3) -----> x = 5/(y+3)

step 2: solve this new equation for y
xy + 3x = 5
xy = 5-3x
y = (5-3x)/x


I was able to find the inverse, but both the original and the inverse have restrictions, so
it is not a one-to-one function
e.g. In the original , if x = -3, there is no value of y, so: not a 1-1
in the inverse, if x = 0 , there is no value of y, so: not a 1-1

Wolfram verification:
http://www.wolframalpha.com/input/?i=plot+y+%3D+5%2F%28x%2B3%29+%2C+x+%3D+5%2F%28y%2B3%29+%2C+y+%3D+x