Questions: Part 3 of 3 (c) c(x) = 1 / sqrt(x+25) The domain in interval notation is .

Solution Steps

To find the domain of the function \( c(x) = \frac{1}{\sqrt{x+25}} \), we need to determine the values of \( x \) for which the expression under the square root is positive, as the square root of a negative number is undefined in the real number system. Additionally, the denominator cannot be zero, so \( x+25 \) must be greater than zero.

1. Set the expression under the square root greater than zero: \( x + 25 > 0 \).
2. Solve the inequality to find the domain of \( x \).

To find the domain of the function \( c(x) = \frac{1}{\sqrt{x+25}} \), we need to ensure that the expression under the square root is positive. This leads us to the inequality: \[ x + 25 > 0 \]

We solve the inequality: \[ x > -25 \] This indicates that \( x \) must be greater than \(-25\) for the function to be defined.

The domain of the function in interval notation is: \[ (-25, \infty) \]

Final Answer