#### Answer

No, the function $ f\left( x \right)=\frac{x+7}{x-7}$ is not continuous at $7$.

#### Work Step by Step

Consider the function $ f\left( x \right)=\frac{x+7}{x-7}$,
First check whether the function is defined at the point $ a $ or not.
Find the value of $ f\left( x \right)$ at $ a=7$,
$ f\left( 7 \right)=\frac{7+7}{7-7}$
The function is not defined at the point $7$.
Thus, the function do not satisfy the first property of being continuous.
Hence, the function $ f\left( x \right)=\frac{x+7}{x-7}$ is not continuous at $7$.