Determine the domain of the function

f as a function of x is equal to the square root of nine minus x

if f(x) = √(9-x)

then 9-x cannot be negative. So,

9-x >= 0
x <= 9

To determine the domain of a function, you need to consider any restrictions on the values of x that would cause the function to be undefined.

In this case, we have the function f(x) = √(9 - x). The square root function is defined for non-negative numbers, so the expression inside the square root (9 - x) must be greater than or equal to 0.

To find the domain, we solve the inequality 9 - x ≥ 0:

9 - x ≥ 0

To isolate x, we subtract 9 from both sides of the inequality:

-x ≥ -9

Next, we divide both sides of the inequality by -1. However, since we are dividing by a negative number, the direction of the inequality sign will flip:

x ≤ 9

Therefore, the domain of the function f is all values of x that are less than or equal to 9. In interval notation, the domain can be written as (-∞, 9].