Question

Let \(f(x)=\begin{cases A+2x,&\text{if }x \\ 1+x^{2},&\text{if }x\ge3 \end{cases}\). 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