2 votes 2 votes 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 $x^{8}-71$ and $x^{8}-71$ $x^{8}-73$ and $x^{8}-73$ $x^{8}+71$ and $x^{8}+71$ $x^{8}+73$ and $x^{8}+73$ Set Theory & Algebra ugcnetcse-dec2014-paper2 discrete-mathematics functions + – makhdoom ghaya asked Jul 18, 2016 recategorized Apr 12, 2020 by Himanshu1 makhdoom ghaya 2.4k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes 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 $(hog)of$. sh!va answered Jul 18, 2016 edited Apr 12, 2020 by Himanshu1 sh!va comment Share Follow See 1 comment See all 1 1 comment reply Sanjay Sharma commented Jul 19, 2016 reply Follow Share actually second part is (hog)of which will also be X^8 +73 so ans is D 2 votes 2 votes Please log in or register to add a comment.
0 votes 0 votes 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 Girjesh Chouhan answered May 2, 2020 Girjesh Chouhan comment Share Follow See all 0 reply Please log in or register to add a comment.