Posted by ellie on Sunday, November 15, 2009 at 2:04pm.
f: R>R defined by f(x)=x is a function but it is neither surjective nor injective because in order to be injective, each real number y that is an element of the function's Y mapping, which in this case is all reals, can only be gotten to by at MOST one possible real number x in the function's X mapping (NOTE: this allows for the possibility that some values can be in the function's Y mapping that cannot be gotten to by any element of the function's X mapping). For the function f(x)=x, there is exactly two elements x of the function's X mapping that correspond to each element y of the function's Y mapping. Therefore, the function cannot be injective. Whereas to be surjective, the function needs to have for every element y of its Y mapping at LEAST one element in its X mapping that corresponds to y (NOTE: this allows for two elements in the function's X mapping to correspond to the same element in the function's Y mapping). Since the function's Y mapping is all reals, including negative real numbers, no negative element of the function's Y mapping can be gotten to by any element of the function's X mapping.
Note the shape of the graph:
\  /
\/



Related Questions
math  If f is a real valued funtion of a real variable defined by: x^2  3x + 2...
maths  example of a function f:z>z that is surjective but not injective
Maths  For two sets X={1,1,a} and Y={7,16,b} f(x)=x^3+8 is a bijective ...
Maths  For 2 sets X={1,2,3,4},Y={−15,0,30}, f is a surjective function ...
Maths  If g(x)>0 for all real values of x, which of the following could be ...
bussiness maths  using the graphical method solve the following linear ...
maths  prove that the following function is differentiable at x=0 using first ...
Science  Which of the following would not be affected by a loss of vacuole ...
maths  The function f is given by ln(e^x − e ^−x) (x > 0). By ...
calculus  In the following problem, suppose f(x) is continuous (and ...