ASSIGNMENT 1·4
There are two parts to this assignment. The first part is on WeBWorK — the link is available on the course
webpage. The second part consists of the questions on this page. You are expected to provide full solutions
with complete arguments and justifications. You will be graded on the correctness, clarity and elegance of
your solutions. Your answers must be typeset or very neatly written. They must be stapled, with your name
and student number at the top of each page.
1. g(x) = sin x is a trigonometric function we will analyze later in the course. Let f (x) =
the domain of the composite function f ◦ g(x).
√
x + 1. Determine
2. Let f (x) = −(1 − x)2 + 2. Find constants a, b and c such that the function g(x) = af (x + b) + c intersects
the curve x2 + 4x + y 2 + 10y + 28 = 0 at exactly one point.
3. A function is called even if f (x) = f (−x) for all x in its domain, and odd if f (x) = −f (−x) for all x in
its domain.
(a) Explain why even functions do not have inverses.
(b) Give an example of an odd function with an inverse, and an odd function with no inverse.
(c) Suppose an odd function f has an inverse g. Prove that g is also odd.