The problem asks to find the domain of the function:

$h(x) = \sqrt{-x + 4}$

Step-by-step solution:

1. The square root function requires its argument to be non-negative (i.e., ≥ 0).

   $-x + 4 \geq 0$

2. Solve for $x$:

   $-x \geq -4$

   Dividing by $-1$ (remember to flip the inequality):

   $x \leq 4$

Domain:

The domain of the function is all $x$ values less than or equal to 4. In interval notation, this is:

$(-\infty, 4]$

This is the domain of $h(x)$.

Would you like further details or explanations?

Here are 5 related questions to explore further:

1. How do we find the range of the function $h(x) = \sqrt{-x + 4}$?
2. What happens to the domain if we modify the function to $h(x) = \sqrt{-2x + 4}$?
3. Can the function $h(x) = \sqrt{-x + 4}$ have any undefined points?
4. How would you find the domain of a function that involves both a square root and a fraction?
5. What changes if we