SOLUTION: If the function f: R → R such that f(x)= x^2 + 1. Is this function surjective? injective (one-to-one)? bijective? Explain.
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Question 1131828: If the function f: R → R such that f(x)= x^2 + 1. Is this function surjective? injective (one-to-one)? bijective? Explain.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
is injective (one-to-one) onto
Injective means we won't have two or more ""s pointing to the same "".
In other words there are two values of that point to one .
Function is said to be injective or one-to-one if every element in the range is an image of at most one element from the domain.
An injective function is called a one-to-one function.
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Add to both sides of the equation:
Take the square root of both sides of the equation to eliminate the exponent on the left side.
=±
The complete solution is the result of both the positive and negative portions of the solution.
,
There is more than y value for some x values, which means that y=x^2+1 is not an equation of a function.
is not surjective onto
A function (from set A to B) is surjective if and only if for every in B, there is at least one in A such that , in other words is surjective if and only if .
In simple terms: every has some .
Surjective (Also Called "Onto")means that every "" has at least one matching "" (maybe more than one).
There won't be a "" left out.
But,
domain is (all real numbers) and
range (codomain) is
{ element : }
So, in this function all the negative values in the codomain of do not have any corresponding values in the domain of
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