How to determine if f(x)= -3x+4 from real numbers to real numbers is injective, surjective, or bijective

The function is injective.

The function is surjective.

The function is bijective.

Explanation:

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

So:

*(-1)

Since if, and only if, , the function is injective.

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

Here we have:

The domain of x is the real numbers, which means that for each value of y, there is a value of x such that . So, the function is surjective.

A function f(x) is bijective when it is both injective and surjective. So this function is bijective.

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