For f(x)=x2, x(-,), find f(f(f(x)))/f(x).

GATE 2020 CE (CE2) – Question 5

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

For $f(x)=x^2$, $x\in(-\infty,\infty)$, find $f(f(f(x)))/f(x)$.

$f(x)$
$(f(x))^2$
$(f(x))^3$
$(f(x))^4$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) $(f(x))^3$

Explanation

Composition gives $f(f(x))=x^4$ and $f(f(f(x)))=x^8$. Dividing by $x^2$ gives $x^6=[f(x)]^3$. **C** for x ≠ 0. The printed quotient is undefined at zero; the simplified expression is its continuous extension.