Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function such that $f(3 x)-f(x)=x$. If $f

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Let $f: \mathbb{R} ightarrow \mathbb{R}$ be a continuous function such that $f(3 x)-f(x)=x$. If $f(8)=7$, then $f(14)$ is equal to\

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(b) : Given that, $f: R ightarrow R$ is continuous and $f(3 x)-f(x)=x$.\ $	herefore \quad \frac{f(3 x)-f(x)}{3 x-x}=\frac{1}{2}$\ Now, by using Lagrange's Mean Value Theorem, we have\ $f^{\prime}(x)=\frac{f(3 x)-f(x)}{3 x-x}=\frac{1}{2} \Rightarrow f^{\prime}(x)=\frac{1}{2}$\ By integrating on both sides, we get\ $f(x)=\frac{1}{2} x+c$\ Now, $f(8)=7$\ [Given]\ $\Rightarrow \quad f(8)=4+c$ i.e., $c=3$\ $	herefore f(x)=\frac{x}{2}+3 \Rightarrow f(14)=7+3=10$\