Q. 7 - Precalculus Enhanced with Graphing Utilities

Question

Find the domain of each function. 

$f\left(x\right)=\sqrt{2-x}$

Step-by-Step Solution

Answer

The domain of the function is $\left\{x\right|x\le 2\}$.

Step 1. Given information

We have been given a function $f\left(x\right)=\sqrt{2-x}$.

We have to find its domain.

Step 2. Find the values that make the function defined

Square root function is defined for nonnegative numbers.

Therefore, $(2-x)$ should be non-negative.

$$\begin{gathered} 2-x\ge 0 \\ 2-x+x\ge 0+x (\mathrm{Add} \mathrm{x} \mathrm{on} \mathrm{both} \mathrm{sides}) \\ 2\ge x \\ x\le 2 \end{gathered}$$

Therefore, the domain is $\left\{x\right|x\le 2\}$.