If a function f : X → Y defined as f(x) = y is one-one and onto, then we can define a unique function g : Y → X such that g(y) = x, where x ∈ X and y = f(x), y ∈ Y. Function g is called the inverse of function f. The domain of sine function is R and function sine : R → R is neither one-one nor onto. The following graph shows the sine function. Let sine function be defined from set A to [– 1, 1] such that inverse of sine function exists, i.e., sin⁻¹ x is defined from [– 1, 1] to A. On the basis of the above information, answer the following questions :

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Domain, Codomain and Range of a Function, Inverse Trigonometric Functions and Their Definitions, Principal Value Branch of Inverse Trigonometric Functions | PadhAiPro

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CASE_STUDIESDomain, Codomain and Range of a FunctionInverse Trigonometric Functions and Their DefinitionsPrincipal Value Branch of Inverse Trigonometric FunctionsCBSE PYQ4 sub-questions

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