Question

Determine the domain of the function.

f as a function of x is equal to the square root of 1-x

Answer 1

Recall that when we take the square root of something,
\(\large\rm \sqrt{\color{orangered}{c}}\)
It's important that that something (the thing in orange), be positive.
We can't take the root of a negative value.
One thing I could say is this: \(\large\rm \color{orangered}{c}\ge0\)
This value c has to be 0 or larger so we can take it's square root.

So we'll apply that same idea to our function!
\[\large\rm f(x)=\sqrt{\color{orangered}{1-x}}\]So we know that the thing under the root has to be 0 or larger,\[\large\rm \color{orangered}{1-x}\ge0\]And we can solve for x in this inequality.