find the domain of the function sin^-1(2x-1)
Answers
Step-by-step explanation:
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Answer:
The domain of the function sin^-1(x) is the set of all real numbers x such that -1 <= x <= 1.
Step-by-step explanation:
In mathematics, the sine function (sin) is a trigonometric function that represents the ratio of the side length of a right triangle opposite to an angle to the hypotenuse. It is usually denoted by the symbol sin(x) or sin x, where x is the angle in radians. The sine function has many important properties and applications in mathematics, physics, engineering, and other fields.
The sin function is periodic, with a period of 2π, and is defined on the interval (-∞, ∞). Its graph is a smooth curve that oscillates between -1 and 1, and it is one of the three fundamental trigonometric functions, along with cosine and tangent.
So for the function sin^-1(2x-1), we need to find the set of all real numbers x such that -1 <= 2x-1 <= 1.
Solving this inequality, we get:
-1 <= 2x-1 <= 1
Add 1 to both sides
0 <= 2x <= 2
Divide both sides by 2
0 <= x <= 1
So the domain of the function sin^-1(2x-1) is x belongs to [0,1]
To learn more about sin, click on the given link.
https://brainly.in/question/218519
To learn more about real numbers, click on the given link.
https://brainly.in/question/379923
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