Answer questions 4 to 7 by using the given functions g and f. Hint: Drawing graphs of f and g before answering the questions, may assist you. Keep in mind that g Z+ Q and f Z+ Z+. Please note that graphs will not be asked for in the exam. Question 6 Which one of the following alternatives represents the image of x under g ￮ f (ie g ￮ f(x)))? 1. 20x2 + 8x – 12 2. 80x2 + 4 x – 3. 20x2 + 8x + 3 4. 80x2 + 4 x – 3 Question 7 Which one of the following statements regarding the function g is TRUE? (Remember, g Z+ Q.) 1. g can be presented as a straight line graph. 2. g is injective. 3. g is surjective. 4. g is bijective.
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Let be a function from (the set of positive integers) to (the set of rational numbers) defined by
and let be a function on defined by
We consider the statements provided in the different alternatives:
1. is not defined on the set of real numbers thus cannot be depicted as a straight line graph.
Only positive integers can be present in the domain of
It is the case that rdered pairs such as belong to and these pairs can be presented as dots in a graph.
2. We prove that is indeed injective:
3. The function is NOT surjective.
We conclude that is not surjective.
4. Since is not surjective, then is not bijective.
2. is injective.