Chapter 2, Problem 11RE

To determine

To find the domain of the function $f\left(x\right)=\sqrt{2-x}$ .

Answer to Problem 11RE

All real numbers $x$ except $x>2$ .

Explanation of Solution

Given:

A function is given as

  $f\left(x\right)=\sqrt{2-x}$

Concept used:

If domain is not specified for a function, the set of largest real number should be considered where the function is defined all over.

For irrational function the expression under even power root should be greater than equal to zero.

Calculation:

Domain of $f\left(x\right)=\sqrt{2-x}$ is the values ofx for which expression under even power root should be greater than equal to zero.

.

That is,

  $\begin{array}{c}2-x\ge 0\\ 2\ge x\\ x\le 2\end{array}$

Hence the domain of $f\left(x\right)=\sqrt{2-x}$ is the set of all real numbers $x$ except $x>2$ .