JEE Mains · Maths · STD 12 - 1. relation and function
Let \(f : R \rightarrow R\) be a continuous function such that \(f(3 x)-f(x)=x\). If \(f(8)=7\), then \(f(14)\) is equal to.
- A \(4\)
- B \(10\)
- C \(11\)
- D \(16\)
Answer & Solution
Correct Answer
(B) \(10\)
Step-by-step Solution
Detailed explanation
\(f(x)-f(x / 3)=x / 3\) \(f(x / 3)-f\left(x / 3^{2}\right)=x / 3^{2}\) \(f(x)-\lim _{n \rightarrow \infty} f\left(\frac{x}{3^{n}}\right)=x\left(\frac{1}{3}+\frac{1}{3^{2}} \ldots \infty\right)\) \(f(x)-f(0)=\frac{x}{2}\) \(f(8)=7 ; f(0)=3\) \(f(x)=x / 2+3\) \(f(14)=10\)
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