Question

Fill in the following table: 1. Function Domain Range arcsin(u) = sin-1(u) arccos(u) = cos-1 (u) arctan(u) = tan-Yu)

Answer 1

Domain of sin^-1 (u): - Def: The domain of a function is the set of input or argument values for which the function is real and defined. Find known functions domain restrictions: - sin^-1 (f(x)) Rightarrow -1 lessthanorequalto f(x) lessthanorequalto 1 Rightarrow - 1 lessthanorequalto u lessthanorequalto 1 Therefore Domain of sin^-1 (u) = -1 lessthanorequalto u lessthanorequalto 1 interval notation = [-1, 1] Range of sin^-1 (u): - Def: The set of values of the dependent variable for which a function is defined \r\n The range of the basic sin^-1 (u) function is -pi /2 lessthanorequalto sin^-1 (u) lessthanorequalto pi/2 Rightarrow -pi/2 lessthanorequalto sin^-1 (u) lessthanorequalto pi/2 The range of sin^-1 (u) = -pi/2 lessthanorequalto f (u) lessthanorequalto pi/2 interval notation = [-pi/2, pi/2]