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

To find the values of \( x \) where the function \( k(x) = e^{\sqrt{x-7}} \) is discontinuous, we need to analyze the expression inside the function. 1. **Identify the domain of the function:** The function \( k(x) \) involves a square root, \( \sqrt{x-7} \). The square root function is defined only for non-negative values. Therefore, we need to ensure that the expression inside the square root is non-negative: \[ x - 7 \geq 0 \] This simplifies to: \[ x \geq 7 \] 2. **Determine the points of discontinuity:** The function \( k(x) \) is composed of the exponential function and the square root function. The exponential function \( e^y \) is continuous for all real numbers \( y \). However, the square root function \( \sqrt{x-7} \) is only defined for \( x \geq 7 \). Therefore, the function \( k(x) \) is discontinuous for values of \( x < 7 \) because the square root is not defined in that range. 3. **Conclusion:** The function \( k(x) \) is discontinuous for all values of \( x < 7 \). Thus, the values of \( x \) where the function is discontinuous are: \[ (-\infty, 7) \]