Question

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

• A. $x$
• B. $-x$
• C. $\frac{1}{x}$
• D. $-\frac{1}{x}$
• E. $0$

Answer 1

The correct option is A $x$

Given, $f\left(x\right)=\frac{x+2}{3x-1}$
Therefore, $f\left\{f\right(x\left)\right\}=f\left(\frac{x+2}{3x-1}\right)=\frac{\frac{x+2}{3x-1}+2}{3\left(\frac{x+2}{3x-1}\right)-1}$
$=\frac{x+2+6x-2}{3x+6-(3x-1)}=\frac{7x}{7}=x$