Questions on how to find domain and range of arccosine functions.
Theorem1. y = arccos x is equivalent to cos y = xwith -1 ? x ? 1 and 0 ? y ? pi Questione with Detailed Solutions
Question 1Find the domain and range of y = arccos(x + 1)
Solution to question 1
Question 2Find the domain and range of y = - arccos(x - 2)
Solution to question 2
We now multiply all terms of the above inequality by - 1 and invert the inequality symbols 0 ? - arcsin(x + 2) ? pi which gives the range of y = - arccos(x + 2) as the interval [0 , pi] Question 3Find the domain and range of y = -2 arccos(- 2 x + 1)
Solution to question 3
We now multiply all terms of the above inequality by - 2 and invert the inequality symbols 0 ? - 2 arccos(3x - 1) ? - 2 pi which gives the range of y = - 2 arccos(- 2x + 1) as the interval [- 2 pi]
Question 4Find the domain and range of y = 2 arccos( 2 x ) + pi/2
Solution to question 4
We now multiply all terms of the above inequality by 2 0 ? 2 arccos(2x) ? 2 pi We now subtract pi/2 to all terms of the above inequality. pi / 2 ? 2 arccos(2x) + pi / 2 ? 5 pi / 2 which gives the range of 2 arccos(2x) + pi / 2 as the interval [ pi / 2 , 5 pi / 2] More References and Links to Inverse Trigonometric FunctionsInverse Trigonometric FunctionsGraph, Domain and Range of Arcsin function Graph, Domain and Range of Arctan function Find Domain and Range of Arccosine Functions Find Domain and Range of Arcsine Functions Solve Inverse Trigonometric Functions Questions |