Jackie S.

asked • 04/03/20# A quadratic function such as y = x^2 is an injection.

## 2 Answers By Expert Tutors

Christopher F. answered • 04/06/20

M.S. Mathematics |Tufts| Math coach for Math/Econ/Engineering majors

y=x^{2} is not an injection because it is not 1-to-1: it fails the horizontal line test.

Another way of looking at it:

If our f(x) is x^{2} then in order for it to be injective f(x_{1})=f(x_{2}) must imply x_{1}= x_{2}

However, f(-1)=f(1) because (-1)^2=(1)^2, but -1≠1. Therefore, it cannot be injective.

Simplest way to tell if a function is injective or not? If you know the graph of the function and every horizontal straight line passes through it once and only once, then you know it's injective.

Hope this helps! If you have any questions in any of the steps, please comment. :)

Patrick B. answered • 04/04/20

Math and computer tutor/teacher

FALSE

horizontal line test fails...

Let A,B be elements of the range such that A^2 = B^2 with A not equal to B

A^2 - B^2 = 0

(A+B)(A-B) = 0

A +B = 0 or A-B = 0

the latter forces A=B which is a contradiction

A+B=0 ---> A = -B ---> B = -A

so f(A) = A^2 and f(-A) = A^2

so for any A in the domain, f(A) = f(-A) = A^2 and so it is NOT one-to-one

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Tim T.

Is this a true or false question?04/03/20