Let . Which ordered triple of functions satisfies where…

MATHEMATICS · Single correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let h(x)=sin⁡((x2−1)3)h(x)=\sin\bigl((x^{2}-1)^{3}\bigr). Which ordered triple (r, q, p)(r,\,q,\,p) of functions satisfies h=p∘q∘rh = p\circ q\circ r where (p∘q∘r)(x)=p(q(r(x)))(p\circ q\circ r)(x)=p\bigl(q(r(x))\bigr)? (a) r(x)=x3,  q(u)=u2−1,  p(v)=sin⁡vr(x)=x^{3},\; q(u)=u^{2}-1,\; p(v)=\sin v (b) r(x)=x2−1,  q(u)=u3,  p(v)=sin⁡vr(x)=x^{2}-1,\; q(u)=u^{3},\; p(v)=\sin v (c) r(x)=x2−1,  q(u)=sin⁡u,  p(v)=v3r(x)=x^{2}-1,\; q(u)=\sin u,\; p(v)=v^{3} (d) r(x)=sin⁡x,  q(u)=u3,  p(v)=v2−1r(x)=\sin x,\; q(u)=u^{3},\; p(v)=v^{2}-1

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