Let be differentiable and invertible with and

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let ff be differentiable and invertible with f(1)=3f(1)=3 and f′(1)=−2f'(1)=-2. Define h(x)=sin⁡(f−1(x))h(x)=\sin\bigl(f^{-1}(x)\bigr). Evaluate h′(3)h'(3). (a) −sin⁡12-\dfrac{\sin 1}{2} (b) −cos⁡12-\dfrac{\cos 1}{2} (c) −cos⁡1-\cos 1 (d) \dfrac{\cos 1}{2}

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