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What is mapping in algebra?
A mapping is a relationship between two sets. Given sets A and B (which need not be different) a mapping allocates an element of B to each element of A.
Prove or disprove if the composition fg is surjective than f and g are surjective?
counter example: f(x)= arctan(x) , f:R ->(-pi/2 , pi/2) g(x)=tan(x) , g:(-pi/2, pi/2) -> R (g(x) isn't surjective) f(g(x))=arctan(tan(x))=x f(g(x)): R -> R Although, if two of the three are surjective, the third is surjective as well.
What is a algebra mapping?
A mapping consists of two sets and a rule for assigning to each element in the first set one or more elements in the second set. We say that A is mapped to B and write this as m: A→B.
What is the domain of algebra?
Among other topics, algebra deals with mappings. These are relations between two sets - which can be the same. A mapping is a process which assigns an element in the second set to each element of the first set. The first set is the domain and the second is the range.For example, if the mapping is "square the number" and the domain is {-3, 1, 2, 3}, then the range would be {9, 1, 4, 9} which is the same as {1, 4, 9}.
What are some function words?
Domain, codomain, range, surjective, bijective, invertible, monotonic, continuous, differentiable.
