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Summary Mat1510 Assignment 2 2024 Solutions

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This document contains MAT1510 ASSIGNMENT 2 2024 SOLUTIONS. Clear step by step calculation are provided.

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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

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