University of Toronto Scarborough MATA31
Assignment # 1-Fall 2025
Read sections 0.1, 0.2, and 0.3.
Solve the following problems. While all are important, submit only those
highlighted in red. Your TA will mark the assignment and return it the next
week. In addition to accuracy, ensure that your solutions include full details
and explanations to avoid losing marks. This assignment is due during the
week of September 15–19, at the beginning of your tutorial, and is worth
4%.
Important note: You must include your first name, last name,
and student number at the top of your solutions and staple all
pages together before submitting.This will help prevent your work
from getting lost.
0.1: 12, 18, 19, 28, 30, 34, 36,40, 42 (Also, provide the range; you
don’t need to graph it.), 44, 48
0.2: 8, 12, 16, 24, 26, 28, 32, 36, 46, 50, 52, , 53, 60, 64, 66, 68, 70,
80, 86, 89, 94
0.3: 2, 4, 6, 10, 16, 18, 28, 30, 36, 40, 46, 52, 56, 58, 60, 78
A.
Prove that
f ◦g+
f2
g3 − g
is an odd function for two odd functions f and g.
B.
√
Show that 3 x5 + k is a one-to-one function where k is a constant.
Then find f −1 .
C. Evaluate f (t2 − 1) if
f (x) =
3,
if x < 1
√
x + 1, if x ≥ 1