MAT1510
ASSIGNMENT 2
2024
, QUESTION 1
Solution:
1.1).
False
Example: Let f(x) = x 2
f(s) = s 2 and f(t) = t 2
f(s + t) = (s + t)2
f(s + t) = s 2 + t 2 + 2st
f(s + t) = f(s) + f(t) + 2st
f(s + t) ≠ f(s) + f(t)
1.2).
False
Example: Let f(x) = x 2
f(−1) = f(1)
(−1)2 = (1)2
, 1 = 1 but 1 ≠ −1
1.3).
False
Example: Let f(x) = x 2
f(3x) = (3x)2 and 3f(x) = 3x 2
f(3x) = 9x 2 and 3f(x) = 3x 2
f(3x) ≠ 3f(x)
1.4).
True
1.5).
False
Example: Let f(x) = x + 1, then
f(x) = x + 1
y =x+1
x =y−1
f −1 (x) = x − 1
and
ASSIGNMENT 2
2024
, QUESTION 1
Solution:
1.1).
False
Example: Let f(x) = x 2
f(s) = s 2 and f(t) = t 2
f(s + t) = (s + t)2
f(s + t) = s 2 + t 2 + 2st
f(s + t) = f(s) + f(t) + 2st
f(s + t) ≠ f(s) + f(t)
1.2).
False
Example: Let f(x) = x 2
f(−1) = f(1)
(−1)2 = (1)2
, 1 = 1 but 1 ≠ −1
1.3).
False
Example: Let f(x) = x 2
f(3x) = (3x)2 and 3f(x) = 3x 2
f(3x) = 9x 2 and 3f(x) = 3x 2
f(3x) ≠ 3f(x)
1.4).
True
1.5).
False
Example: Let f(x) = x + 1, then
f(x) = x + 1
y =x+1
x =y−1
f −1 (x) = x − 1
and
