Question

The function $f\left(x\right)$ satisfies the condition $(x-2)f\left(x\right)+2f\left(\frac{1}{x}\right)=2$ for all $x\ne 0$. Then the value of $f\left(2\right)$ is

• A. $\frac{1}{2}$
• B. $1$
• C. $\frac{7}{4}$
• D. $\frac{-3}{2}$

Answer 1

The correct option is B $1$

Putting $x=2$ in $(x-2)f\left(x\right)+2f\left(\frac{1}{x}\right)=2$

$(2-2)f\left(2\right)+2f\left(\frac{1}{2}\right)=2$

$2f\left(\frac{1}{2}\right)=2$

$f\left(\frac{1}{2}\right)=1$