Question

What is the domain of g(x)=−x−−√3+5 ?(1 point) Responses −∞≤y≤∞ negative infinity less-than-or-equal-to y less-than-or-equal-to infinity −∞<x<∞ negative infinity less than x less than infinity 0≤y≤∞ 0 less-than-or-equal-to y less-than-or-equal-to infinity 0<x<∞

Answer 1

To determine the domain of the function \( g(x) = -\sqrt{x} + 3 + 5 \), we first simplify the function:

\[ g(x) = -\sqrt{x} + 8 \]

The expression \(-\sqrt{x}\) is only defined for non-negative \(x\), meaning \(x\) needs to be greater than or equal to 0:

\[ x \geq 0 \]

Therefore, the domain of \(g(x)\) is:

\[ [0, \infty) \]

In interval notation, this is written as \(0 \leq x < \infty\).

So, the correct response is \(0 \leq x < \infty\).