First slide

Functions (XII)

Question

If $A = \{x : \frac{- 2}{5} \leq x \leq \frac{π - 2}{5}\}, B = \{y : - 1 \leq y \leq 1\}$ and $f (x) = \cos (5 x + 2)$ then the mapping $f : A \to B$ is

Moderate

A

One-one but not onto
B

Onto but not one - one
C

Both one - one and onto
D

Neither one - one nor onto

Solution

Let $t = 5 x + 2, t h e n A = \{t : 0 \leq 1 \leq π\}$
$∴ f (t) = \cos t$ which is bijective in $[0, π]$
Hence f(x) is bijective

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