Q. 56 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 47– 62, find the domain of each function. 

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

Step-by-Step Solution

Answer

The domain of the given function is $\left\{x\right|x\le -1\}$

Step 1. Given Information

In the given problems we have to find the domain of given function.

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

Step 2. The function G tells us to take the square root of 1 - x .

But only non-negative numbers have real square roots, so the expression under the square root (the radicand) must be non-negative (greater than or equal to zero).

Step 3. This requires that

$1-x\ge 0$

Subtract 1 on both side

$$\begin{gathered} 1-x+1\ge 0+1 \\ -x\ge 1 \end{gathered}$$

multiply with $-1$ on both side and change the inequality

$$\begin{gathered} -x\times (-1)\le 1\times (-1) \\ x\le -1 \end{gathered}$$

Step 4. The domain of G is

$\left\{x\right|x\le -1\}$