If f(x) = (5x+2)/(3x-5) and g(x) = x 2 – 2x – 1, then the value of g(f(f(3))) is:

Question

If f(x) = (5x+2)/(3x-5) and g(x) = x 2 &ndash; 2x &ndash; 1, then the value of g(f(f(3))) is:

Accepted Answer

2 — Easy Evaluate from the inside out: $f(3)$, then $f$ of that, then apply $g$. Watch for the neat collapse $f(f(3))=3$. 1 Compute $f(3)$. $$\begin{aligned} &f(3) = \frac{5(3)+2}{3(3)-5} = \frac{17}{4} \end{aligned}$$ 2 Compute $f\!\left(	frac{17}{4}ight)$. Multiply numerator and denominator through by $4$. $$\begin{aligned} &f\!\left(	frac{17}{4}ight) = \frac{5\cdot\frac{17}{4}+2}{3\cdot\frac{17}{4}-5} = \frac{85+8}{51-20} = \frac{93}{31} = 3 \end{aligned}$$ 3 Apply $g$ to the result. So $f(

CAT 2017 Slot 1 — QA Question 33

Answer & solution

Related Composite Functions questions