Question

If $f\left(x\right)=\frac{5x+2}{3x-5}$ and $g\left(x\right)=x^2-2x-1$, then the value of $g\left(f\right(f\left(3\right)\left)\right)$ is

• A. $2$
• B. $\frac{1}{3}$
• C. $6$
• D. $\frac{2}{3}$

Answer 1

The correct option is A

$2$

$f\left(3\right)=\frac{(5\times 3+2)}{(3\times 3-5)}=\frac{17}{4}f\left(f\right(3\left)\right)=\frac{(5\times \left(\frac{17}{4}\right)+2)}{(3\times \left(\frac{17}{4}\right)-5)}=3g\left(f\right(f\left(3\right)\left)\right)=g\left(3\right)=9-6-1=2$.