Download GRE Quick Reference Guide For f to be function from A to B Domain

GRE Quick Reference Guide
 For f to be function from A to B
1. Domain of f = A
2. No Repetition in the domain
 Onto, if range of f = B
 Let f be a function whose domain is a set A. The function f is injective if for all a and b in A,
if f(a) = f(b), then a = b; that is, f(a) = f(b) implies a =b. Equivalently, if a ≠ b, then f(a) ≠ f(b).
 An injective function
 Another injective function (this one is a bijection)
 A non-injective function (this one happens to be a surjection)
 An injective function (one-to-one) and a bijective function (one-to-one correspondence)
 The composition of two injective functions is injective
 In mathematics, a function f is said to be surjective or onto, if its values span its
whole codomain; that is, for every y in the codomain, there is at least one x in the domain such
that f(x) = y .
 Said another way, a function f: X → Y is surjective if and only if its range f(X) is equal to its
codomain Y. A surjective function is called a surjection.
 A surjective function. (However, this one is not an injection)
 Another surjective function. (This one happens to be a bijection)
 A non-surjective function. (This one happens to be an injection)
 Surjective composition: the first function need not be surjective.
 In mathematics, a bijection, or a bijective function is a function f from a set X to a set Y with the
property that, for every y in Y, there is exactly one x in X such that
f(x) = y. Alternatively, f is bijective if it is a one-to-one correspondence between those sets; i.e.,
both one-to-one (injective) and onto (surjective). (One-to-one function means one-to-one
correspondence (i.e., bijection) to some authors, but injection to others.)
 A bijection composed of an injection (left) and a surjection (right)
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One-One, for different first element there should be different second element
Into,
Non-terminating and non-recurring decimal fraction are called irrational numbers
Surds
Log2 8 = 3 → 23 = 8
Logamn = nLogam
LogbN = LogaN / Logab
(a+b)2 = a2 + b2 + 2ab = (a - b)2 + 4ab
(a-b)2 = a2 + b2 - 2ab = (a + b)2 - 4ab
a2 – b2 = (a + b)(a - b)
(x +a)(x + b) = x2 +ab + (a+b)x
(a + b + c)2 = a2 + b2 + c2 +2ab + 2bc + 2ca
(a +b)3 = a3 + b3 + 3ab(a +b)
(a -b)3 = a3 - b3 - 3ab(a -b)
a3 + b3 = (a +b)(a2 + b2 + ab)
a3 - b3 = (a -b)(a2 + b2 + ab)
a3 +b3 + c3 -3abc = (a +b +c)(a2 + b2 + c2 –ab –bc -ca)
area of ellipse = πr1r2
if divided by x – 3, P (3) = 0, then x – 3 is factor
 distance =
( x2  x1 )2  ( y2  y1 )2
Analytical
 Simplify the information and term using abrevation and symbols
 Abbrevate a single word and a sentence too
 Use symbol to represent a condition
 Use elimination strategy
 Condition must be understood explicitly and also what they imply to
 Some time a diagram is also helpful
 ”Must be true” means ti identify a true choice, other choice may or may not be true
 “Could be true” means to identify a true choice, other choices must be false
Logical Reasoning
 Read the question before reading the passage
 Study well the last and first sentence of the passage
 Pay attention and mark the signal (hence, although, because, but etc) words
 Use elimination strategy
 Every argument is based on an assumption. If basic assumption is sound, the argument is
strengthened, if flawed, then weakened
Sentence Completion
 Do not look at the choices, try to think on your own and then check
 In case of two blanks, select a suitable choice for the first blank and then fill the second, then
make intersection of the two
Analogy
 First study relationship between the pair
 Choices must have same grammatical order as pair
 Major Relationships are
 Synonym
 Antonym
 Describing qualities
 Describing intensity
 Class member
 Function
Critical Reading
 First read the passage
 Mark lines and words
 If stuck, solve next, which may be helpful in the first