If f(x) = and g(x) = sin π x + 8 where {·} denotes fracti…

Maths Functions, Limits, Continuity and Differentiability General Subjective Type

Published on: August 13, 2026

If f(x) = and g(x) = sin π x + 8 where {·} denotes fractional part function then the find range of f(g(x))

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The correct answer is:

CHECK THE SOLUTION.

Sol. As g(x) is periodic with period 2 so f(g(x)) is periodic with period 2.

Now g(x) = sin π x + g = sin π x + 8 · 0 ≤ x < 2

g(x) = sin π x + 4x ; 0 ≤ x < 2 ⇒ g'(x) = π cos π x + 4 .

so g(0) = 0 and g(2 – ) = 8 so, g(x) ∈ [0, 8)

so range of f(g(x)) is ≡ .

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