Question 4800 – UGC NET CS 2014 Dec-Paper-2

If we define the functions f, g and h that map R into R by :
f(x) = x⁴ , g(x) = √ x² + 1 , h(x) = x² + 72, then the value of the composite functions ho(gof) and (hog)of are given as

Correct Answer: D

Question 5 Explanation:

Given f(x) = x ⁴ , g(x) = √ x ² + 1 , h(x) = x 2 + 72
for, ho(gof)
gof=g(f(x))
=g(x ⁴ )
=√(x ⁸ +1)
ho(gof)=h(gof)
=h(√(x ⁸ +1))
=(√(x ⁸ +1) 2 +72
=x ⁸ +1+72
=x ⁸ +73
√ x ² + 1 , h(x) = x² + 72
for, (hog)of,
hog=h(g(x))
=h(√(x ² +1)
=(√(x ² +1) 2 +72
=x ² + 1+72
=x ² +73
(hog)of=(hog)(f(x))
=(hog)(x ⁴ )
=(x ⁴ ) ² +73
=x ⁸ +73
Hence, option-D is the correct answer

x ⁸ – 71 and x ⁸ – 71

x ⁸ – 73 and x⁸ – 73

x ⁸ + 71 and x ⁸ + 71

x ⁸ + 73 and x ⁸ + 73

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