Question

Write the range of the function f(x) = sin [x], where \[\frac{- \pi}{4} \leq x \leq \frac{\pi}{4}\] . 

Answer 1

Given that,

`f(x) = sin|x|`

where `(-pi)/4 le x le pi/4`

we divide the range into two parts,

(a) `(-pi/4)< x < 0`

`⇒ |x| = -1`

Then `f(x) = sin(-1) = - sin 1`

(b) `0 < x < (pi/4)`

`⇒ |x| = 0`

Then, `f(x) = sin0 = 0`

Thus, the range of f(x) becomes {0, −sin1}