Questions: Find the domain and range of the given function. Explain your answers. f(x)=-5/(√(10-x)) What is the domain of the function? A. All real numbers x<10 B. All real numbers x ≥ 10 C. All real numbers x>10 D. All real numbers x ≤ 10

Solution Steps

To find the domain of the function \( f(x) = \frac{-5}{\sqrt{10-x}} \), we need to ensure that the expression inside the square root is non-negative and the denominator is not zero. This means \( 10 - x > 0 \), which simplifies to \( x < 10 \). Therefore, the domain is all real numbers \( x < 10 \).

We are given the function \( f(x) = \frac{-5}{\sqrt{10-x}} \). To determine the domain, we need to analyze the expression under the square root.

The expression \( \sqrt{10-x} \) must be defined and non-negative. Therefore, we require: \[ 10 - x > 0 \] This simplifies to: \[ x < 10 \]

The domain of the function is all real numbers \( x \) such that \( x < 10 \). In interval notation, this can be expressed as: \[ (-\infty, 10) \]

Final Answer