Derivatives of Inverses #6

Question

State the domain and range of each of the following functions:

(a)  has

Domain: 

Range: 

(b)  has

Domain: 

Range: 

(c)  has

Domain: 

Range: 

Answer 1

The range is rule-driven.

For the domain, we just consider the range of the inverse of the function

a) Domain is the range of cos(x), [-1, 1]

Range is [0, π]

b) Domain is the range of sin(x), [-1, 1]

Range is [-π/2, -π/2]

c) Domain is the range of tan(x), (-∞, ∞)

Range is (-π/2, -π/2)

Note how the endpoints are not part of the range, because tan is not defined there.