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Consider three functions, f(x)=x3+x2+x+1, g(x)=2xx2+1 and h(x)=sin−1x−cos−1x+tan−1x−cot−1x and let p(x) be a differentiable function on R defined as p(x)={a∫x0√p(t)dt+b;x>0x2+4x+1;x≤0 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)(m−7)=(S)5 h(g(f(x))) is kπ2, then |k| is equalto Which of the following option is the only correct combination? |
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Answer» Consider three functions, f(x)=x3+x2+x+1, g(x)=2xx2+1 and h(x)=sin−1x−cos−1x+tan−1x−cot−1x and let p(x) be a differentiable function on R defined as p(x)={a∫x0√p(t)dt+b;x>0x2+4x+1;x≤0 where, a, b ϵ(0,∞) and tangent drawn to the graph of p(x) at x = 1 is y = mx + c |
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