State the domain and range of the function: g(x) = 1 - √x?

Question

Please explain

Answer 1

domain:
x>=0

range:
x>=0,
√x>=0
-√x<=0
1-√x<=1
so the range are all the numbers y<=1

Answer 2

Domain = x values
Since the square root of a negative x would result in an irrational number, the implied domain (for all real number answers) must be:
Implied Domain = 0 to positive infinity or [0, + infinity)

Range = g(x) or y values
Since the domain is restricted to 0 to infinity, the y is also restricted in the equation. For 0, the y = 1-0 or y=1. y approaches negative infinity as x approaches positive infinity so:
Range = 1 to negative infinity or [1, - infinity)

Answer 3

Domain: can't take the square root of a negative number, so must have x >= 0. This is the domain.

Range: sqrt(x) >= 0, so -sqrt(x) <= 0, so 1-sqrt(x) <= 1.

Therefore, the range is y <= 1.