UGC NET CSE | January 2017 | Part 2 | Question: 3

Question

The functions mapping $R$ into $R$ are defined as :

$f\left(x \right)=x^{3} - 4x, g\left(x \right)=\frac{1}{x^{2}+1}$ and $h\left(x \right)=x^{4}.$

Then find the value of the following composite functions :

$h_{o}g\left(x \right)$ and $h_{o}g_{o}f\left(x \right)$

• A. $\left ( x^{2}+1 \right )^{4}$ and $\left [ \left ( x^{3}-4x \right )^{2}+1 \right ]^{4}$
• B. $\left ( x^{2}+1 \right )^{4}$ and $\left [ \left ( x^{3}-4x \right )^{2}+1 \right ]^{-4}$
• C. $\left ( x^{2}+1 \right )^{-4}$ and $\left [ \left ( x^{2}-4x \right )^{2}+1 \right ]^{4}$
• D. $\left ( x^{2}+1 \right )^{-4}$ and $\left [ \left ( x^{3}-4x \right )^{2}+1 \right ]^{-4}$

Answer 1

option 4

 

h(g(x))=h(1/(x^2 +1)) = (x^2 +1)^ -4

h(g(f(x)))= h(g(x^3 -4x)) = [(x^3-4x)^2+1]^ – 4

Comments

$f \circ g (x)$  is defined as $f (g (x))$

your answer is correct , please use equation editor to type set equations properly

Answer 2

Option D is right

h o g(x) = h(g(x)) = h(1/x² +1) = (x²+1)^-4

h o g o f(x) = h(g(f(x))) = h(g(x³ - 4x)) = h(1/[(x³ - 4x)² +1]) = [(x³ - 4x)² +1]^-4

Answer 3

Ans is D