$\text{ Consider } f(x) = \begin{cases} 2 \sin(a \cos^{-1} x), & \text{if } x \in (0, 1) \\ \sqrt{3}, & \text{if } x = 0 \\ ax + b, & \text{if } x < 0 \end{cases}$ …

Mathematics

Problem

\text{ Consider } f(x) = \begin{cases} 2 \sin(a \cos^{-1} x), & \text{if } x \in (0, 1) \\ \sqrt{3}, & \text{if } x = 0 \\ ax + b, & \text{if } x < 0 \end{cases}

Assertion (Statement I): If

b = \sqrt{3}

and

a = \frac{2}{3}

, then

f(x)

is continuous in

(-\infty, 1)

. Reason (Statement II): If a function is defined on an interval

I

and limit exists at every point of interval

I

, then function is continuous in

I