Chapter 2.1, Problem 56AYU

In Problems 51-66, find the domain of each function.

$G\left(x\right)=\sqrt{1-x}$

To determine

To find: The domain of the function $G\left(x\right)=\sqrt{1-x}$.

Answer to Problem 56AYU

Domain of $G=\{x|x\le 1\}$, or the interval $\left(-\infty ,1\right]$.

Explanation of Solution

Given:

The function $G\left(x\right)=\sqrt{1-x}$.

Calculation:

The function $G$ says to take the square root of $1-x$. But only nonnegative numbers have real square roots, so the expression under the square root (the radicand) must be nonnegative (greater than or equal to zero). This requires that

$1-x\ge 0$

$-x\ge -1$

$x\le 1$

The domain of $G$ is $\{x|x\le 1\}$, or the interval $\left(-\infty ,1\right]$.