Question

Find the range of f(x) = $1/2|cosx|-3$

Answer 1

Answer:

Hence range of f(x) is [-3, - 5/2]

Step-by-step explanation:

Here

$f(x) = \frac{1}{2} | \cos(x) | - 3$

We know that

$- 1 \leqslant \cos(x) \leqslant 1$

$or \: 0 \leqslant | \cos(x) | \leqslant 1$

$or \: 0 \leqslant \frac{1}{2} | \cos(x) | \leqslant \frac{1}{2}$

$or \: - 3 \leqslant \frac{1}{2} | \cos(x) | - 3 \leqslant \frac{1}{2 } - 3$

$or \: - 3 \leqslant f(x) \leqslant - \frac{5}{2}$

Hence range of f(x) is [-3, - 5/2]