Questions: Determine the domain of the function represented by the given equation. (Enter your answer using interval notation.) f(x)=sqrt1-x

Solution Steps

To determine the domain of the function \( f(x) = \sqrt{1-x} \), we need to find the set of all \( x \) values for which the expression under the square root is non-negative. This is because the square root function is only defined for non-negative numbers. Therefore, we solve the inequality \( 1-x \geq 0 \).

The given function is \( f(x) = \sqrt{1-x} \). This is a square root function, and the expression inside the square root must be non-negative for the function to be defined.

To find the domain, we need to ensure that the expression inside the square root is greater than or equal to zero:

\[ 1 - x \geq 0 \]

Solve the inequality \( 1 - x \geq 0 \):

\[ 1 \geq x \]

or equivalently,

\[ x \leq 1 \]

The solution to the inequality \( x \leq 1 \) is all real numbers less than or equal to 1. In interval notation, this is expressed as:

\[ (-\infty, 1] \]

Final Answer