Question

How do find the domain of cos x ?

Answer 1

Domain of the function f(x) is set of all numbers if we put in f(x) in place of x then the value f(x) will exist. If we put x equal to 0 in the function $\dfrac{1}{x}$ the value will tend to infinity, so 0 is not in the domain of $\dfrac{1}{x}$. We will find out all such x for which cos x will not be defined.

Complete step by step answer:
We have to find the domain of cos x
Let’s draw the graph of cos x and find all such x for which cos x is not defined

We can see that the graph of cos x is a continuous curve for all values of x from $-\infty$ to $+\infty$ , there is no such value for which the function cos x is not defined. So the domain of cos x is from $-\infty$ to $+\infty$ .

Note:
We have seen how we can find the domain of some function, if we were given a composite function f(g(x)) and we have to find the domain of it. We can solve it by first finding the domain of g(x), let’s take the domain of g(x) that is set a. Then we have to find the domain of f(x) let’s take it set b. Then we have find set all the x for which g(x)=b , let’s call it set c. our answer that means domain of f(g(x)) is intersection of set a and set c which is $a\cap c$