find the domain and range of the function. f(x)=|4x| - cos 4x the domain is □. (type your answer in interval…
find the domain and range of the function. f(x)=|4x| - cos 4x the domain is □. (type your answer in interval notation.)
Answer
Explanation:
Step1: Analyze domain of absolute - value part
The absolute - value function (y = |4x|) is defined for all real numbers (x), i.e., (x\in(-\infty,\infty)).
Step2: Analyze domain of cosine part
The cosine function (y=\cos(4x)) is also defined for all real numbers (x), (x\in(-\infty,\infty)).
Step3: Determine domain of the whole function
Since both (|4x|) and (\cos(4x)) are defined for all real (x), the domain of (f(x)=|4x|-\cos(4x)) is the set of all real numbers.
Answer:
((-\infty,\infty))