Question
Fri April 08, 2011 By: Ashwini Kumar

check the following function for injectivity and surjectivity.

Expert Reply
Fri April 08, 2011
f(x) = x(x+1)(x-1)

A function f is said to be surjective or onto, if for every y in the codomain, there is at least one x in the domain such that f(x) = y.

as y =f(x) = x^3- x = x(x^2-1)

It takes the value from -infinite to + infinite and contnuous so for each y there is an x and hence it is surjective

A function f from A to B is said to be injective if different elements in A have different images in B.

Now, f(-1) = f(0) = f(1) = 0, so f cannot be injective.
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