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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.
