**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]