Science:Math Exam Resources/Courses/MATH220/April 2011/Question 01 (a)

MATH220 April 2011

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Question 01 (a)
Let $\displaystyle f:A\to B$ be a function and let $C\subseteq A$ and $D\subseteq B$. Define the sets $\displaystyle f^{-1}(D)$ and $\displaystyle f(C)$.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
Recall that $\displaystyle f^{-1}(D)$ is the pre-image of the set $D$, that is the set containing all the elements that are mapped by $f$ into the set $D$ and that $\displaystyle f(C)$ is the image of the set $C$, that is the set all the images of elements of the set $C$.

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Solution
Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. $f^{-1}(D)=\{a\in A\mid f(a)\in D\}$ and $f(C)=\{f(c)\mid c\in C\}.$

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