in Quantitative Aptitude recategorized by
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2 votes

If $f(x) = x^2$ for each $x\in (-\infty,\infty)$, then $\large \dfrac{f\left(f\left(f(x)\right)\right)}{f(x)}$ is equal to _______.

  1. $f(x)$
  2. $(f(x))^2$
  3. $(f(x))^3$
  4. $(f(x))^4$
in Quantitative Aptitude recategorized by
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1 Answer

1 vote
1 vote
Best answer
Given that, $f(x) = x^{2}.$

Now, $f\left(f\left(f(x)\right)\right) = f\left(f\left(x^{2}\right)\right) = f\left(x^{4}\right) = x^{8}$

$\therefore \dfrac{f\left(f\left(f(x)\right)\right) }{f(x)} = \dfrac{x^{8}}{x^{2}} = x^{6} = (x^{2})^{3} =  (f(x))^{3}.$

So, the correct answer is $(C).$
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