Let f : R R be a function defined by f(x) = (2x + 5), then f is: - Vidyadip

MCQ

Let $f : R \times R$ be a function defined by $ \text{f}(\text{x}) = \cos(2\text{x} + 5)$, then $f$ is:

A
injective
B
surjective
C
bijective
✓
None of these

✓

Answer

Correct option: D.

None of these

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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