Question

find the domain of the function.
(h(x)=sqrt{-x + 7})
write your answer as an inequality.
or, you may instead click on \empty set\ or \all reals\ as the answer.

Explanation:

Step1: Set the radicand non - negative

For the square - root function $y = \sqrt{u}$, the radicand $u$ must satisfy $u\geq0$. Here, $u=-x + 7$, so we set up the inequality $-x + 7\geq0$.

Step2: Solve the inequality for $x$

Add $x$ to both sides of $-x + 7\geq0$, we get $7\geq x$, which is equivalent to $x\leq7$.

Answer:

$x\leq7$