Asked by Anonymous
Determine if the function is onto, if not find an element of the codomain that is not in the range. I have no clue where to begin with this. I appreciate any help.
g:R-->[1,infinity) given by g(x)=x^2+1
g:R-->[1,infinity) given by g(x)=x^2+1
Answers
Answered by
Steve
Read the introduction in wikipedia explaining the difference between range and codomain.
For example, if
g:R->R g(x)=x^2, then the codomain is all of R, but the range (image) is [0,∞)
For this problem, g is onto, since both the codomain and the image are [1,∞). There is no element of [1,∞) such that g(x) cannot be found there.
For example, if
g:R->R g(x)=x^2, then the codomain is all of R, but the range (image) is [0,∞)
For this problem, g is onto, since both the codomain and the image are [1,∞). There is no element of [1,∞) such that g(x) cannot be found there.
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