Question

If, $\{\begin{array}{cc}\frac{3a}{2}x-(a+1)& ;x\ne 2\\ 1& ;x=2\end{array}$ is continuous at $x=2$, then $a=$ _____

• A. $2$
• B. $-1$
• C. $1$
• D. $0$

Answer 1

Answer: (C)

$1$

If $f\left(x\right)$ is continuous at $x=2$, then

putting $x=2$ in $\frac{3a}{2}x-(a+1)$ gives

$\frac{3a}{2}2-(a+1)=1$

$⟹2a-1=1$

$⟹a=1$