UGC-NET | UGC NET CS 2017 Jan – II | Question 3

The functions mapping R into R are defined as :
f(x) = x³ – 4x, g(x) = 1/(x² + 1) and h(x) = x⁴.
Then find the value of the following composite functions :
hog(x) and hogof(x)
(A) (x² + 1)⁴ and [(x³ – 4x)² + 1]⁴
(B) (x² + 1)⁴ and [(x³ – 4x)² + 1]^-4
(C) (x² + 1)^-4 and [(x³ – 4x)² + 1]⁴
(D) (x² + 1)^-4 and [(x³ – 4x)² + 1]^-4


Answer: (D)

Explanation:

 f(x) = x3 – 4x, g(x) = 1/(x2 + 1) and h(x) = x4
 hog(x) = [g(x)]4
        =  [1/(x2 + 1)]4
        =  [(x2 + 1)-1]4
        =  [(x2 + 1)]-4
Similarly:
hogof(x) = [gof(x)]4
         = [(f(x)2 + 1)]-4
         =  [((x3 – 4x)2 + 1)]-4

So, option (D) is correct.

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