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If we define the functions $f$, $g$ and $h$ that map $R$ into $R$ by : 

$f(x)=x^{4}, g(x)= \sqrt{x^{2}+1}, h(x)=x^{2}+72$, then the value of the composite functions $ho(gof)$ and $(hog)of$ are given as

  1. $x^{8}-71$ and $x^{8}-71$
  2. $x^{8}-73$ and $x^{8}-73$
  3. $x^{8}+71$ and $x^{8}+71$
  4. $x^{8}+73$ and $x^{8}+73$
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Answer D.

f(x) = $x^4$,     g(x) = $\sqrt{x^2 +1}$,      h(x) = $x^2 + 72$

gof = g($x^4$) = $\sqrt{x^8 +1}$

$ho(gof)$ = h($\sqrt{x^8 +1}$) = $(\sqrt{x^8 +1})^2$  +72 = $x^8 + 73$

Similarly, we can calculate $(hog)of$.
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Sol. is D

Well, composition of functions satisfies the associative property.

That implies ho(gof) = (hog)of. Thus, finding only ho(gof) will solve the problem.

But, solved the ques. to show, how compositions can be solved..!!
The

Answer:

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