Find all values of \( x \) where the function is discontinuous. \( k(x)=e^{\sqrt{x-7}} \)

The function \( k(x)=e^{\sqrt{x-7}} \) is discontinuous where the expression inside the square root is non-positive. Since the square root function is only defined for non-negative values, we have the restriction: \[ \sqrt{x-7} \text{ is defined for } x-7 \geq 0 \Rightarrow x \geq 7. \] Thus, the function is continuous for \( x \geq 7 \) and undefined for \( x < 7 \). Therefore, the function is discontinuous at all values \( x < 7 \). In summary, the function \( k(x) \) is discontinuous for \( x < 7 \), and specifically, it is important to note that at \( x = 7 \) it actually becomes continuous. In conclusion, the values of \( x \) where the function \( k(x) \) is discontinuous are: \[ (-\infty, 7). \]