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CGP EDU Academic Team
Published on: August 12, 2026
Let f : R → [–1, 1] be a function
f(x) = cos (sin 3x + 4 sin 3 x).
(i) Range of function is –
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Ans.
(i)
Sol. f(x) = cos (sin 3x + 4sin 3 x)
f(x) = cos (3sinx) = cos(3t)
where sin x = t, t ∈ [–1, 1]
range is [cos 3, 1]
(ii)
Sol. f(x) = cos (3 sin x) clearly 2 π is a period
but f( π + x) = cos (3 sin ( π + x)) = cos ( – 3 sin x)
= cos (3 sin x )
∴ π is also a period, π /2 is not a period hence fundamental period is π
(iii)
Sol. Since f(x) is periodic so it is many-one and range 
co-damian
into
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