Question

If $f\left(x\right)=\{\begin{array}{c}K{x}^2\text{if}x\le 2\\ 3\text{if}x>2\end{array}$ is continuous at $x=2,$ then the value of $K$ is

• A. $3$
• B. $4$
• C. $\frac{3}{4}$
• D. $\frac{4}{3}$

Answer 1

The correct option is C $\frac{3}{4}$

Given that $f$ is continuous at $x=2.$
$f\left(2^{+}\right)=f\left(2\right)=f\left(2^{-}\right)$
$4K=3\Rightarrow K=\frac{3}{4}$