Classify the following functions as injection, surjection or bije… - Vidyadip

Question

Classify the following functions as injection, surjection or bijection:
f : R → R, defined by f(x) = sin²x + cos²x

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Answer

f : R → R, defined by f(x) = sin²x + cos²x
f(x) = sin²x + cos²x = 1
So, f(x) = 1 for every x in R.
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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