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

Option: 1

\mathrm{4}


Option: 2

\mathrm{10}


Option: 3

\mathrm{11}


Option: 4

\mathrm{16}


Answers (1)

best_answer

\mathrm{f(x)-f\left(\frac{x}{3}\right)=\frac{2 x}{3}} \\

\mathrm{f\left(\frac{x}{3}\right)-f\left(\frac{x}{3}\right)=\frac{x}{3^{2}}}         ............on adding

\mathrm{f(x)=\lim _{n \rightarrow \infty} f^{\prime}\left(\frac{x}{3^{n}}\right)=x\left(\frac{1}{3}+\frac{1}{3^{2}}+\cdots, \infty\right)} \\

\mathrm{f(x)-f(0)=\frac{x}{2}} \\

\mathrm{f(8)=7, f(0)=3} \\

\mathrm{f(x)=\frac{x}{2}+3} \\

\mathrm{f(14)=10}

Hence correct option is 2

 

Posted by

manish painkra

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