Question

What is the domain and range of y=cos|x|?

Answer 1

Answer:

The domain of y=cos|x| is R(-∞,∞) and its range is [-1,1]

Step-by-step explanation:

The given trigonometric function is

$y = cos |x|$

x can take any real values such as 0,30,15,45,-120 etc..

When negative values of x are taken they become positive due to the relation mentioned below

$|x| = x \: if \: x \geqslant 0 \\ = - x \: if \: x < 0$

Therefore the domain is R(-,-).

As we know that domain,the range of cosx is already known which is [-1,1] because

$- 1 \leqslant cosx \leqslant 1$

Therefore,The domain of y=cos|x| is R(-∞,∞) and its range is [-1,1]

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