CBSE NET JANUARY 2017 PAPER II
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)
(1) (x2+1)4 and [(x3-4x)2+1]4
(2) (x2+1)4 and [(x3-4x)2+1]- 4
(3) (x2+1)- 4 and [(x3-4x)2+1]4
(4) (x2+1)‑ 4 and [(x3-4x)2+1]- 4
Ans: (4)
Explanation:
hog(x) = h(1/(x2+1))
= [(1/(x2+1))]4 = (x2+1)- 4
hogof(x) = hog(x3-4x)
= hog(x3-4x)
= [(x3-4x)2+1]- 4 [since hog(x) = (x2+1)- 4]