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Question
Classify the following function as injection, surjection or bijection :
f : R → R, defined by f(x) = sinx
Solution
f : R → R, defined by f(x) = sinx
Injection test :
Let x and y be any two elements in the domain (R), such that f(x) = f(y).
f(x) = f(y)
sin x = sin y
Here, x may not be equal to y because sin0=sinπ.So, 0 and π have the same image 0 .
So, f is not an injection .
Surjection test :
Range of f = [-1, 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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