How to determine if the function f(x) = x^2 + 3 from real numbers to real numbers is injective, surjective, or bijective

The function is not injective.

The function is not surjective.

The function is not bijective.

Explanation:

A function f(x) is injective if, and only if, when .

So

Since we may have when, for example, , the function is not injective.

A function f(x) is surjective, if, and only if, for each value of y, there is a value of x such that .

We have that y is composed of all the real numbers.

Here we have:

There is only a value of x such that for . So the function is not surjective.

A function f(x) is bijective when it is both injective and surjective. So this function is not bijective.

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