SOLUTION: Determine whether or not the function is one to one. f (x)=x^2-3

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Question 968784: Determine whether or not the function is one to one.
f (x)=x^2-3
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

by definition, injective (or one-to-one) means that every member of "A" has its own unique matching member in "B"
To show that f is 1-1, you could show that
f%28x%29=f%28y%29 => x=y
one example: suppose f%28x%29=%28x-3%29%2F%28x%2B2%29
then%28x-3%29%2F%28x%2B2%29=%28y-3%29%2F%28y%2B2%29
%28x-3%29%28y%2B2%29=%28y-3%29%28x%2B2%29
+cross%28xy%29%2B2x-3y-cross%286%29=cross%28+yx%29%2B2y-3x-cross%286%29
2x-3y=2y-3x
2x%2B3x=2y%2B3y
5x=5y
x=y...so,f%28x%29 is 1-1

in your case f+%28x%29=x%5E2-3 , so if x%5E2-3=y%5E2-3 then f+%28x%29 is 1-1
x%5E2-3=y%5E2-3
x%5E2-3%2B3=y%5E2
x%5E2=y%5E2
=>x=y or -x=y...so,f%28x%29 is not 1-1, it is not injective (one-to-one) on its domain


In fact we can do a "Horizontal Line Test":

as you can see, x=-2 and x=2 have same y=1