one to one function

1

Take the function you want to check. For example, you might want to check f(t) = t-3/t+2.

1. 2
   Make functions f(x) and f(y) from f(t). To do this, change the variable t first to xand then to y. That way, you can perform the test with two different variables. So, in this example:
   

   • f(x) = x-3 / x+2
   • f(y) = y-3 / y+2
2. 3
   Set your two functions as equal. In this example, then: x-3 / x+2 = y-3 / y+2
3. 4
   Simplify the equation by cross multiplication. Cross multiplying the above equation results in an equation that looks like this: (x-3)(y+2) = (y-3)(x+2)
4. 5
   Simplify further by eliminating the parentheses. Multiplying the terms yields the following equation: yx+2x-3y-6 = yx-3x+2y-6
5. 6
   Continue simplifying. Keep simplifying as follows:
   

   • yx+2x-3y-6 = yx-3x+2y-6
   • 2x-3y = -3x+2y
   • 2x+3x = 2y+3y
   • 5x = 5y
   • x = y
6. 7
   Check whether x comes out equal to y. If so (like in the example above), the function is indeed one to one. If not, the function is not one to one.
7. wikihow