Mathematics - Continuity - Differentiability Question with Solution | TestHub

Since the function is continuous at $x=1$, we have LHL = RHL.

$$1=a+{\sin }^{-1}(1+b)$$

Since the function is differentiable at $x=1$, we have LHD = RHD.

$$1=\frac{1}{\sqrt{1-(1+b{)}^2}}$$

This implies $1-(b+1{)}^2=1$, which simplifies to $b=-1$.

Substituting $b=-1$ into the continuity equation, we get $a=1$.