Question

Let \[ f(x)= \begin{cases} A+2x, & \text{if } x<3,\\[4pt] 1+x^{2}, & \text{if } x\ge3. \end{cases} \] If the function \(f(x)\) is continuous at \(x=3\), then the value of \(A\) is: 

• A. \(1\)
• B. \(6\)
• C. \(10\)
• D. \(4\)

Hint:

For piecewise functions, \[ \boxed{ \text{Continuity} \Longrightarrow \text{LHL}=\text{RHL}=f(a) } \] Always calculate the left-hand expression and right-hand expression separately before equating them.

Answer 1

The Correct Option is D