find the domain and range of the function. f(x)=|x| - cos x the domain is (type your answer in interval…

Answer:

The domain is $(-\infty,\infty)$ The range is $[- 1,\infty)$

Explanation:

Step1: Determine the domain

The functions $y = |x|$ and $y=\cos x$ are defined for all real - numbers. So, the domain of $f(x)=|x|-\cos x$ is all real numbers, written as $(-\infty,\infty)$ in interval notation.

Step2: Analyze the range

We know that $-1\leqslant\cos x\leqslant1$. Also, $|x|\geqslant0$. When $x = 0$, $f(0)=|0|-\cos(0)=0 - 1=-1$. As $|x|$ increases without bound, $|x|-\cos x$ also increases without bound since $\cos x$ is bounded between $-1$ and $1$. So the range of $f(x)$ is $[-1,\infty)$.