SOLUTION: f:R to R f(x)=x ^2 is it surjective function??? if f:N to N then is the above function surjective??

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Question 906388: f:R to R f(x)=x ^2 is it surjective function??? if f:N to N then is the above function surjective??
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
To be surjective, every number in the second set must be
obtainable by choosing a number in the first set and substituting
it for x in the equation f(x)=x2.

f:R to R f(x)=x2 is it a surjective function??? 
No.  The first and second sets are both R. No value of x in the 
first set R will result in a negative number when you square it.
Thus, for instance, the number -4 is in the second set R, but 
there is no number in the first set, that you can substitute
for x in f(x)=x2 and get -4.

if f:N to N then is the above function surjective??
No because no number in the first set N when squared gives 
2,3,5,6,7,8,10,... or any non-square integer, yet those non-square 
integers are all in the second set N.

Edwin