Let f : R → R be a continuous function such that f(3 x)-f(x)=x . If f(8)=7 , then f(14) is equal t

English

Gujarati

Hindi

1.Relation and Function

hard

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

$16$

(JEE MAIN-2022)

Solution

$f(x)-f(x / 3)=x / 3$

$f(x / 3)-f\left(x / 3^{2}\right)=x / 3^{2}$

$f(x)-\lim _{n \rightarrow \infty} f\left(\frac{x}{3^{n}}\right)=x\left(\frac{1}{3}+\frac{1}{3^{2}} \ldots \infty\right)$

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

$f(8)=7 ; f(0)=3$

$f(x)=x / 2+3$

$f(14)=10$

Standard 12

Mathematics

Share

Similar Questions

The domain of definition of the function $y(x)$ given by ${2^x} + {2^y} = 2$ is

easy

(IIT-2000)

If $f:\left\{ {1,2,3,4} \right\} \to \left\{ {1,2,3,4} \right\}$ and $y=f(x)$ be a function such that $\left| {f\left( \alpha \right) – \alpha } \right| \leqslant 1$,for $\alpha \in \left\{ {1,2,3,4} \right\}$ then total number of such functions are

normal

Let $f(x)$ and $g(x)$ be two functions given by $f\left( x \right) = \frac{{2\sin \pi x}}{x}$ and $g\left( x \right) = f\left( {1 – x} \right) + f\left( x \right).$ If $g\left( x \right) = kf(\frac{x}{2})f\left( {\frac{{1 – x}}{2}} \right)$,then the value of $k$ is

normal

Set $A$ has $3$ elements and set $B$ has $4$ elements. The number of injection that can be defined from $A$ to $B$ is

easy

Which of the following function is even function

medium