Question

If $f\left(\sqrt{\left(\frac{x-1}{x+1}\right)}\right)=3x,$ then the value of $f\left(3\right)$ is :

• A. $-\frac{15}{4}$
• B. $\frac{\sqrt{2}}{2}$
• C. $9$
• D. $0$

Answer 1

The correct option is A $-\frac{15}{4}$

$1\left(\sqrt{\frac{x-1}{x+1}}\right)=3x$

$\Rightarrow \sqrt{\frac{x-1}{x+1}}=3\Rightarrow \frac{x-1}{x+1}=9$

$x-1=9x+9$

$-8x=10\Rightarrow x=\frac{-5}{4}$

$f\left(3\right)=3\left(\frac{-5}{4}\right)=\frac{-15}{4}$