First slide

Functions (XII)

Question

The function $f : R \to R$ given by $f (x) = 3 - 2 \sin x$ is

Moderate

A

one-one
B

onto
C

bijective
D

none of these

Solution

$- 1 \leq \sin x \leq 1 \Rightarrow 1 \leq f (x) \leq 5 \Rightarrow f (x)$ is not onto, $f (x) = f (x + 2 π) \Rightarrow f$ is not one-one and $f$ is not bijective

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