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Question
Classify the following function as injection, surjection or bijection :
f : R → R, defined by f(x) = sin2x + cos2x
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Solution
f : R → R, defined by f(x) = sin2x + cos2x
f(x) = sin2x + cos2x = 1
So, f(x) = 1 for every x inR.
So, for all elements in the domain, the image is 1.
So, f is not an injection.
Range of f = {1}
Co-domain of f = R
Both are not same.
So, f is not a surjection and f is not a bijection.
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