Question

If \( f(x)= \begin{cases x^2+k, & x\leq 1 \\ 2x+1, & x>1 \end{cases} \) is continuous at \( x=1 \), then the value of \( k \) is:}

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

For piecewise functions, continuity at the "break point" means the function's value, left-hand limit, and right-hand limit at that point must all be equal. This usually boils down to setting the two function expressions equal at the break point.

Answer 1

The Correct Option is B