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Jun 2, 2016 · $\begingroup$ $f((x,y))$ is the "more correct" notation for tuples $(x,y)$ in general. There is no such a thing as a 1-tuple (unless you deliberately define it), since $A^1 = A$ for a set $A$.
Aug 2, 2024 · A function f is a relation that assigns a single value in the range to each value in the domain. In other words, no x -values are repeated.
- f(x) = |x
- f(x) = x
- f(x) = c, where c is a constant
- f(x) = x2
Oct 3, 2022 · For \(f(x) = \sqrt{1-2x}\), \(f(0) = 1\) and \(f(x) = 0\) when \(x = \frac{1}{2}\) For \(\ f(x)=\frac{3}{4-x}, f(0)=\frac{3}{4}\) an \(\ f(x)\) ) is never equal to 0; For \(\ f(x)=\frac{3 x^{2}-12 x}{4-x^{2}}, f(0)=0\) an \(\ f(x)=0\) when \(\ x = 0\) or \(\ x = 4\) \(\ f(-4)=1\) \(\ f(-3)=2\) \(\ f(3)=0\) \(\ f(3.001)=1.999\) \(\ f(-3.001)=1.999\)
f (x) is the result of applying the function f to an object x. I think that by far the most common form of abuse of notation is conflating a structure with its underlying set. If you have a group G, for instance, you'll write x ∈ G to mean that x is an element of the underlying set of G.
A function f is a relation that assigns a single value in the range to each value in the domain. In other words, no x -values are repeated.
You used to say "y = 2x + 3; solve for y when x = −1". Now you say "f (x) = 2x + 3; find f (−1)" (pronounced as "f-of-x equals 2x plus three; find f-of-negative-one"). In either notation, you do exactly the same thing: you plug −1 in for x, multiply by the 2, and then add in the 3, simplifying to get a final value of +1.
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Identify the domain of a function, and evaluate a function from an equation. Gain familiarity with piecewise functions. Study the vertical line test. Know how to form and use composite functions. Order of elements does not matter. E.g. f1; 2; 3g = f3; 2; 1g. Representation of a set is not unique. E.g. f 2; 2g = fx j x2 = 4g. 2: belongs to.
