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What is a relation in which each x-value has one and only one y-value?
It is a surjective relationship. It may or may not be injective, and therefore, bijective.
Is every on-to function a one-one function?
No. The function y = x2, where the domain is the real numbers and the codomain is the non-negative reals is onto, but it is not one to one. With the exception of x = 0, it is 2-to-1. Fact, they are completely independent of one another. A function from set X to set Y is onto (or surjective) if everything in Y can be obtained by applying the function by an element of X A function from set X to set Y is one-one (or injective) if no two elements of X are taken to the same element of Y when applied by the function. Notes: 1. A function that is both onto and one-one (injective and surjective) is called bijective. 2. An injective function can be made bijective by changing the set Y to be the image of X under the function. Using this process, any function can be made to be surjective. 3. If the inverse of a surjective function is also a function, then it is bijective.
What is a A relationship that assigns exactly one output value to one input value?
It is a injective relationship. However, it need not be surjective and so will not be bijective. It will, therefore, not define an invertible function.
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 are some function words?
Domain, codomain, range, surjective, bijective, invertible, monotonic, continuous, differentiable.
What is a relation in which each x-value has one and only one y-value?
It is a surjective relationship. It may or may not be injective, and therefore, bijective.
What is an input or output relation that has exactly one output for each input?
A one-to-one function, a.k.a. an injective function.
Is every on-to function a one-one function?
No. The function y = x2, where the domain is the real numbers and the codomain is the non-negative reals is onto, but it is not one to one. With the exception of x = 0, it is 2-to-1. Fact, they are completely independent of one another. A function from set X to set Y is onto (or surjective) if everything in Y can be obtained by applying the function by an element of X A function from set X to set Y is one-one (or injective) if no two elements of X are taken to the same element of Y when applied by the function. Notes: 1. A function that is both onto and one-one (injective and surjective) is called bijective. 2. An injective function can be made bijective by changing the set Y to be the image of X under the function. Using this process, any function can be made to be surjective. 3. If the inverse of a surjective function is also a function, then it is bijective.
What is a A relationship that assigns exactly one output value to one input value?
It is a injective relationship. However, it need not be surjective and so will not be bijective. It will, therefore, not define an invertible function.
Is the principal trignometric functions are injective?
Yes, that is why they are called "principal". The domains are restricted so that the functions become injective.
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 an isomorphism?
To get a definition you can go to google.com and type in the words define isomorphism or whatever you want defined. isomorphismA map or function taking a structure A (such as a group, ring, field, etc.) exactly onto another similar structure B , so that both A (considered as a substructure of B ) and B look exactly the same. In other words, an isomorphism is an embedding that is surjective as well as injective. See the Related Link. Identical atoms of other elements.
What are some function words?
Domain, codomain, range, surjective, bijective, invertible, monotonic, continuous, differentiable.
What has the author Chi-Te Tsai written?
Chi-Te Tsai has written: 'Report on injective modules ...'
A relation in which each element in the domain is mapped to exactly one element inthe range?
It is an injective relation.
What is surjective in algebra mapping?
A mapping, f, from set S to set T is said to be surjective if for every element in set T, there is some element in S such that it maps on to the element in T. Thus, if t is any element of T, there must be some element, s, in S such that f(s) = t.
What is the relationship between two quantities for each input there is exactly one output.?
The relationship is called a surjection or a surjective function.
