find the domain of the given function
f(x)=square root 9-x
You know that sqrt(u) has domain u>=0. In this case, u = 9-x. So, yu must have
9-x >= 0
9 >= x
or, as usually written
x <= 9
or
{x:x<=9}
or
x in (-oo,9]
depending on desired notation.
To find the domain of the given function f(x) = √(9 - x), we need to determine the values of x for which the function is defined.
First, we look at the expression inside the square root, which is 9 - x. For the function to be defined, the radicand (9 - x) must be non-negative, since we cannot take the square root of a negative number.
So, we set 9 - x ≥ 0 and solve for x:
9 - x ≥ 0
-x ≥ -9
x ≤ 9
Therefore, the domain of the function is all real numbers x such that x ≤ 9. In interval notation, the domain can be expressed as (-∞, 9].
In conclusion, the domain of the function f(x) = √(9 - x) is (-∞, 9].