If 3 f(x)-2 fleft(frac{1}{x}right)=x,then f^{ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given equation is $3 f(x)-2 f\left(\frac{1}{x}\right)=x$ ...$(i)$Replace $x$ with $\frac{1}{x}$ in Eq. $(i)$:$3 f\left(\frac{1}{x}\right)-2 f(x)=\

Vedclass · Accepted Answer

$\frac{1}{2}$

Vedclass · Answer

(A) Given equation is $3 f(x)-2 f\left(\frac{1}{x}\right)=x$ ...$(i)$Replace $x$ with $\frac{1}{x}$ in Eq. $(i)$:$3 f\left(\frac{1}{x}\right)-2 f(x)=\frac{1}{x}$ ...(ii)To eliminate $f\left(\frac{1}{x}\right)$,multiply Eq. $(i)$ by $3$ and Eq. (ii) by $2$:$9 f(x)-6 f\left(\frac{1}{x}\right)=3 x$ ...(iii)$-4 f(x)+6 f\left(\frac{1}{x}\right)=\frac{2}{x}$ ...(iv)Adding Eq. (iii) and Eq. (iv):$5 f(x)=3 x+\frac{2}{x}$$f(x)=\frac{3 x}{5}+\frac{2}{5 x}$Differentiating with respect to $x$:$f^{\prime}(x)=\frac{3}{5}-\frac{2}{5 x^2}$Now,substitute $x=2$:$f^{\prime}(2)=\frac{3}{5}-\frac{2}{5(2)^2} = \frac{3}{5}-\frac{2}{20} = \frac{3}{5}-\frac{1}{10}$$f^{\prime}(2)=\frac{6-1}{10} = \frac{5}{10} = \frac{1}{2}$

If $3 f(x)-2 f\left(\frac{1}{x}\right)=x$,then $f^{\prime}(2)$ is equal to

Similar Questions

If $5 f(x) + 3 f\left(\frac{1}{x}\right) = x + 2$ and $y = x f(x)$,then $\frac{dy}{dx}$ at $x = 1$ is equal to

Find the derivative of the function: $\frac{x}{1+\tan x}$

If $f(x) = \log(\sec x + \tan x)$,then $f^{\prime}\left(\frac{\pi}{4}\right) = $

Let $f$ be a differentiable function such that $f(1) = 2$ and $f'(x) = f(x)$ for all $x \in R$. If $h(x) = f(f(x))$,then $h'(1)$ is equal to

If $f(x) = x^2 - 3x$,then the points at which $f(x) = f'(x)$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module