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Relations and Functions — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSRelations and Functions1 Mark
MCQ
Let f : R × R be a function defined by $ \text{f}(\text{x}) = \cos(2\text{x} + 5)$, then f is:
  • A
    injective
  • B
    surjective
  • C
    bijective
  • D
    None of these
✓

Answer

  1. None of these

Solution:

Given, $ \text{f}(\text{x}) = \cos(2\text{x} + 5)$

Period of $\text{f}(\text{x})=\frac{2\pi}{5}$

Since f(x) is a periodic function with period $\text{f}(\text{x})=\frac{2\pi}{5}$ so it is not injective.

The function f is not surjective also as its range [-1, 1] is a proper subset of its co-domain R.

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