SOLUTION: Determine whether the following functions are surjective.
f(x)=|2x+5|
g(x)=-sqrt(x^2+1)
h(x)=x^3+7
i(x)=x^2+x+1
Algebra.Com
Question 643982: Determine whether the following functions are surjective.
f(x)=|2x+5|
g(x)=-sqrt(x^2+1)
h(x)=x^3+7
i(x)=x^2+x+1
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Use the following intuitive definition of surjective to answer your questions.
A function f is surjective if it ‘hits’ everything in the target set; in your case the target set is Z, so a surjective function is one that ‘hits’ every integer. In less informal language this means that if n is any integer whatsoever, n=f(m) for at least one integer m.
In the case of all of your example functions, the target set is the set of all real numbers, 
. So your "is this surjective?" question reduces to "are there any real numbers excluded from the range of the function?" and a "no" answer implies surjectivity.
John
My calculator said it, I believe it, that settles it
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