Answer
Domain: $\color{blue}{(-\infty, 2]}$
Work Step by Step
To find the domain of the given function, exclude the values of $x$ that will make the function undefined.
Note that the function is undefined when the radicand (expression inside the radical sign) is negative. This is because the square root of a negative number is an imaginary number.
This means that the value of $x$ can be any real number that will make the radicand greater than or equal to zero.
Thus,
$2-x \ge 0
\\-x \ge 0-2
\\-x \ge -2$
Multiply by $-1$ on both sides of the inequality.
Note that this will flip the inequality symbol to the opposite direction.
$x \le -2(-1)
\\x \le 2$
Thus, the value of $x$ can be any real number less than or equal to $2$
.
In interval notation,
Domain: $\color{blue}{(-\infty, 2]}$
