Mathematics 20
17 April 2023
Problems
2nd Semester AY 2022-2023
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General Directions: Provide what is asked for in each item. Show complete solutions and box your final
answers. Work independently.
I. Sketch and give the domain and range of the following function:
1.

3x2 − 18x + 15




x−1

5
1
f (x) =
2x + 2


x2



|2x − 10|
x < −5
−5 ≤ x < −2
−2 ≤ x < 2
2≤x≤8
II. Determine whether the following functions are even or odd:
1 4
x + 3x2
16
2. f (x) = −5x5 + 3x3 − x
1. f (x) =
3. f (x) = |x| − 3
√
x2
x + 2, find the domain of f ◦ g.
and
g(x)
=
x2 − 1
√
IV. Find the domain, range, and inverse of the one-to-one function f (x) = 4x − 1.
III. Given the functions f and g defined by f (x) =
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“We are what we repeatedly do. Excellence, therefore, is not an act but a habit.” - Aristotle
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