is the function a one to one?

Question

f(x)=1/(x^2−1)

 

i have to explain if its a one to one and why. i have no idea

Answer 1

A function is one to one if each different input for x results in a different output for f(x).  If you can find 2 different x values that result in the same value for f(x) then the function is not one to one (it is called many to one).  In this case, if you put in 3 for x you get  

 

f(3) = 1/(3^2 - 1) = 1/8  

 

and if you put in -3 for x you also get  

 

f(-3) = 1/((-3)^2 - 1) = 1/8  

 

so this function is not one to one.