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