Class 12 Relations And Functions · Mcq Single Correct1 Markstypes_of_functions

Class 12 Maths · Relations And Functions · Mcq Single Correct #20

If \(f:\mathbb{R}\to\mathbb{C}\) is defined by \(f(x)=e^{2ix}\) for \(x\in\mathbb{R}\), then \(f\) is (where \(\mathbb{C}\) denotes all complex numbers)

(A) One-one
(B) Onto
(C) One-one and onto
(D) Neither one-one nor onto

✅ Step-by-Step Solution

Final Answer: Option (D): Neither one-one nor onto

The function has period \(\pi\), so it is not injective. Its image is the unit circle, a proper subset of \(\mathbb{C}\), so it is not onto.

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Class 12 Maths · Relations And Functions · Mcq Single Correct #20

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