CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Consider three functions, f(x)=x3+x2+x+1, g(x)=2xx2+1 and h(x)=sin1xcos1x+tan1xcot1x and let p(x) be a differentiable function on R defined as p(x)={ax0p(t)dt+b;x>0x2+4x+1;x0 where, a, b ϵ(0,) and tangent drawn to the graph of p(x) at x = 1 is y = mx + c
 Column 1 Column 2 Column 3(I)If range of f(g(x)) is [l,m],(i)a=(P)1 then (l+m)=   (II)The number of integers in the(ii)b=(Q)3 range of g(f(x)) is equal to   (III)The maximum value of(iii)|c|=(R)4 g(h(x)) is equal to   (IV)If the minimum value of(iv)(m7)=(S)5 h(g(f(x))) is kπ2, then |k| is equalto   
Which of the following option is the only correct combination?


  1. (IV), (ii), (S)

  2. (III), (iii), (Q)

  3. (IV), (iv), (S)

  4. (III), (ii), (S)


Solution

The correct option is C

(IV), (iv), (S)


Range of f(g(x)) = [f(–1), f(1)]
= [0, 4]
Range of g(f(x)) = [–1, 1]
g(h(x))|max=1, where x=1
h(g(f(x)))|min=5π2, when g(f(x)) =-1
p(x)={4x2+4x+1;x>0x2+4x+1;x0
   a = 4, b = 1, c = –3, m = 12

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More



footer-image