Q3Multiple correct4 Marks3 Aug 2025

Consider the functions $f(x)=\begin{cases}x-6,&x<6\\x-7,&x\ge 6\end{cases}$ and $g(x)=\begin{cases}(x-6)^2,&x<6.5\\(x-7)^2,&x\ge 6.5\end{cases}$. Which of the following statements is/are correct?

A

$f$ is not continuous.

B

$f$ is continuous.

C

$g$ is not continuous.

D

$g$ is continuous.