Write out all functions f: {1,2} –→ {a,b, c} (in two-line notation). How many functions are there? How many are injective? How many are surjective? How many are bijective?

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Q: show that A0 subset f-1 (f(A0)) and that equality holds if f is injective

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Q: 1. Let f be the function defined by f(x)=/x+ 2 . Prove that f is one-to-one .

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Q: Prove that f-1 of = Idom f iff f-1 is a function from ran f to dom f.

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Q: Does there exist a function f such that f(0) = -9, f(2) = 9, and f'(x) 5 7 for all x? O Yes O No

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Q: Prove that f is an identity function of itself.

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: