Chapter 4.6, Problem 65E

Solution

To determine : The domain and range of the function $f\left(x\right)=\left|x\right|+\cos x$ .

The domain of the given function is $\left(-\infty ,\infty \right)$ and its range is $\left[1,\infty \right)$ .

Given information :

The function $f\left(x\right)=\left|x\right|+\cos x$ .

Concept used:

The domain of a function is the set of all the real values for which the function is meaningful and range of a function is the set of all real values taken by the function at points in its domain.

Explanation :

Consider the given function $f\left(x\right)=\left|x\right|+\cos x$ .

Graph the given function in the viewing window $\left[-4\pi ,4\pi \right]$ by $\left[-10,20\right]$ .

  

From the graph it is evident that the function is defined for all values of $x$ , and the function assumes all real values greater than or equal to $1$ .

Therefore, the domain of the given function is $\left(-\infty ,\infty \right)$ and its range is $\left[1,\infty \right)$ .