46.6k views
4 votes
Find the range and natural domain of the function f(x)=Sinx ^

1 Answer

3 votes

Answer:

the range of the function (f(x) = \\sin(x)^2) is (\[0, \\infty)), and the natural domain is (\\mathbb{R}) (all real numbers)

Explanation:

The function (f(x) = \\sin(x)^2) represents the square of the sine of (x).

To find the range and natural domain of the function:

1. Natural Domain:

The natural domain of the function (f(x) = \\sin(x)^2) is all real numbers since the sine function is defined for all real values of (x).

Natural Domain: (\\mathbb{R}) (all real numbers)

2. Range:

To determine the range, we need to examine the possible values that (\\sin(x)^2) can take. Since the square of any real number is always nonnegative (greater than or equal to zero), the range of (f(x) = \\sin(x)^2) is the set of nonnegative real numbers.

Range: (\[0, \\infty)) (all nonnegative real numbers)

Therefore, the range of the function (f(x) = \\sin(x)^2) is (\[0, \\infty)), and the natural domain is (\\mathbb{R}) (all real numbers).

User Cyclomarc
by
8.1k points

No related questions found