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  • <img alt="\mathrm{f(x)=\left\{\begin{array}{ll} a+\sin ^{-1}(x+b), & x \geq 1 \\ x, & x<1 \end{array} \text { is differentiable at } x=1,\right. \text { then }}" src="https://entrancecor

\mathrm{f(x)=\left\{\begin{array}{ll} a+\sin ^{-1}(x+b), & x \geq 1 \\ x, & x<1 \end{array} \text { is differentiable at } x=1,\right. \text { then }}

Option: 1

a=1, b=1


Option: 2

a=-1, b=-1


Option: 3

a=1, b=-1


Option: 4

\text { none of these }


Answers (1)

best_answer

Slope of \sin ^{-1} x=1 only when x=0. This means we must shift point (0,0)\, \, to \, \, (1,1)\, \, for \, \, y=\sin ^{-1} x, then shifted curve becomes y-1=\sin ^{-1}(x-1) \Rightarrow a=1 \, \, and \, \, b=-1.

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Gaurav

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