Does the equation above represent a relation, a function, both a relation and a function, or neither a relation nor a function? \n \n\n a.relation only \n b.function only \n c.both a relation and a function \n d.neither a relation nor a function
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Where's the function?
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(a) Suppose f is NOT injective, that is, f( x') = f(x'') for some x' and x'' in X. Then also g(f( x')) = g(f( x'')), which means that g o f is NOT injective. (This is proof by transposition: instead of showing directly that A implies B, we show that Not B implies Not A.)\n\n(b) Take any t in T. Then t = g(f(x)) for some x (since g o f is surjective). This means that t = g(y) for some y, namely, for y = f(x). So g is surjective.\n\n(c) By Part (a), f is injective. By Part (b), applied to f o g in place of g o f, f is surjective. Beig both injective and surjective, f is bijective.
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When you use either/or, or neither/nor, the verb must agree with the subject that is closest to it. B and C as you have typed them here are both correct. Hopefully you will apply that knowledge to your other homework items and do them yourself.
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Sorry I'm not english spoken\n\nIl suffit de choisir deux vecteurs u et v non nuls et non liés.\nu ∧ v ≠ 0\nOn constate alors que :\n(u ∧ u) ∧ v = 0 ∧ v = 0\nSupposons que :\nu ∧ (u ∧ v) = 0\nAlors\nu et u ∧ v sont liés\nCe qui est absurde car :\nu ∧ v ⊥ u\nDonc :\nu ∧ (u ∧ v) ≠ 0\nD'où :\n(u ∧ u) ∧ v ≠ u ∧ (u ∧ v)
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a... NO\nb. NO\nc.  ???\nd. no\ne. no\nNONE OF THE ABOVE
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'x>y' means x is larger than y\n\n'x<y' means x is smaller than y \n\ni hope that this helps
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poly-more than one\nmono-only one.
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It's many years since I did maths but shouldn't there be an = somewhere? And isn't there normally "y" too? I thought it would be fun to stretch my brain for a change but...Am I being obtuse?
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It means that the value of the function f at x is an element of the set containing only the number 3, so f(x)=3.\n\nFor example, if it was R+ instead of {3} with an additional statement "for all x in R" then it would mean that the function only takes on non-negative values for all real numbers.
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It is an equation, the result of the equation is the function. The result may be plotted and it would be a linear function. The plot is a function of the form (equation). It is linear only if it works out to a stright line, which this does.\n\n"A linear function of x is a function of the form y = ax + b, where a and b are constants.  It's called a "linear" function because a plot of the x and y coordinates for which this equation is true takes the shape of a straight line"
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Assume there is a pair a_i, b_j with a non zero product.\nWrite fg= (a_i x^i + other terms) (b_j x^j + other terms) =\na_i b_j x^(i+j) is non zero.\n\nContradiction.
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[i]  = I\n[d]s = does (without the s it would be do)\n[t]  = to or the\n[o] = of\n\nAnyway I think all the [ ] are suppose to be abbreviations and these are the most likely.◘
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f(x)=Int(f'(y), 0, x)-f(0) => yes, they're opposite operation, but if x has a given value, e.g. x=2, 3...no, they're not, b/c in that case, the RHS of the previous egality is a real number, not a function
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Here is an outline:\n\nf is an ONTO function. So for EVERY element b in B there is an\nelement a in A so that f(a) = b.  That is what onto means.  All the\nelements in B have some element in A that f maps it into.\n\nSince g is not one to one there must be two elements  in B that get mapped into the same element in C.  Call them b1 and b2. Show that b1 and b2 are part of the codomain of f.  f(x) maps into all B, so there must be a a1 and a2 that get mapped into b1 and b2.  So then we have g(f(a1)) and g(f(a2) that map into the same element, and hence g(f(x)) is not one to one.
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Please explain what is ~f.  I have curiosity, because neither inverse multiplicative, complex conjugate or inverse function could do that result...\n\nIt should be interesting!! Please post what is ~f !
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dependent.\nyou can't solve one equation without the other equation.
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Yes it is a function because the two variables have a 'one-to-one' relationship, which means that for  every value of x, you can get one and only one value of 'y'. If this one-to-one relationship exists then its called a function.\n  Ex.\n   If x=1, y=3\n   If x=23, y=47 etc.