Chapter 1.4, Problem 10QR

Solution

To find: The domain of a function in interval notation.

The interval $\left(-\infty ,\infty \right)$ is the domain of the function $g\left(x\right)=2$ .

Given information: The function is $g\left(x\right)=2$ .

Method/Formula used:

Suppose $y=f\left(x\right)$ be a function $f:A\to B$ , $x\in A,y\in B$ the set A is called the domain of function f and set B the co-domain. Thus, the domain of a function $f\left(x\right)$ are the values of x for which the function $f\left(x\right)$ is defined.

  

Calculation:

The given function is $g\left(x\right)=2$ .

Since, the function $g\left(x\right)=2$ is a constant, its value is 2 for every real number $x\in \left(-\infty ,\infty \right)$ . Therefore, the interval $\left(-\infty ,\infty \right)$ is the domain of the function $g\left(x\right)=2$ .

The graph of the function $g\left(x\right)=2$ is shown in Fig. (1).