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← JEE Main 2022 · 26 Jul · Shift 1
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JEE Main 2022 · 26 Jul · Shift 1, Mathematics question 1

Let f:R→Rf:\mathbf R\to\mathbf R be a continuous function such that f(3x)−f(x)=xf(3x)-f(x)=x. If f(8)=7f(8)=7, then f(14)f(14) is equal to :

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Answer and worked solution

Official answer: B

Solve. f(x)=x2+cf(x)=\frac x2+c works (f(3x)−f(x)=xf(3x)-f(x)=x); continuity rules out other solutions. f(8)=7f(8)=7 gives c=3c=3, so f(14)=10f(14)=10.

(B)

Topics:Types of functionsContinuity
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