Use interval notation to represent the domain and range of t

Use interval notation to represent the domain and range of the following functions. a. f(a) = arcsin (a) Domains Range b. g(c) = arccos (c) Domains Range c. h(e) = arctan(e) Domains Range

Solution

a. f(a)=arcsin(a)

arcsin function lies between -1 and 1

Therefore domain is [-1,1]

and range is [-pi/2,pi/2]

b. g(c)=arccos(c)

The domain is same for arccosine function that is [-1,1]

And the range is [0,pi].

c. h(e)=arctan(e)

Here there is no restriction on arctangent function

Therefore domain is all real numbers and range is (-pi/2,pi/2)