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Let $f\left ( x \right )=x^{2}$ and $g\left ( x \right )=2^{x}$, for all real $x$. Then the value of $  f \left ( f\left ( g\left ( x \right ) \right )+g\left( f\left ( x \right ) \right ) \right)$  at $x=1$ is

  1. $16$
  2. $18$
  3. $36$
  4. $40$
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Given that,     $f(x)=x^{2}$ and $g(x)=2^{x};\forall x\in \mathbb{R}$

Now, we can find the functions value which is required.

  • $f(1)=1^{2}= 1 $
  • $g(1)=2^{1}= 2 $
  • $f(2)=2^{2}= 4 $
  • $f(6)=6^{2}= 36 $

 The value of $f(f(g(x))+g(f(x)))$  at $x=1 : $

Now, $f(f(g(1))+g(f(1)))= f(f(2)+g(1)) =f(4+2)=f(6) =36$

$\therefore$ The value of $f(f(g(x))+g(f(x)))$  at $x=1$ is $36.$

Correct Answer $:\text{C}$

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