Question

what is the domain for f as a function of x is equal to the square root of one minus x.

Answer 1

\[f(x) = \sqrt{1-x}\]

What does the domain of a function mean?
A domain of a function represents all 'x' values which are applicable.

So, to find out which 'x' values are applicable here, we essentially find out, any restrictions imposed on 'x' or not.

Well, f(x) = \(\sqrt{1-x}\), implies that:
anything under the root, is always greater than or equal to zero.

That means, 1 - x \(\ge\) 0
which implies that,

x \(\le\) 1

So the domain of x, D = \((-\infty , 1]\)