Answer:
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:
[tex]f(x) = -3x + 4[/tex]
[tex]f(a) = f(b)[/tex]
[tex]-3a + 4 = -3b + 4[/tex]
[tex]-3a = -3b[/tex] *(-1)
[tex]3a = 3b[/tex]
[tex]a = \frac{3b}{3}[/tex]
[tex]a = b[/tex]
Since [tex]f(a) = f(b)[/tex] if, and only if, [tex]a = b[/tex], 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:
[tex]f(x) = y[/tex]
[tex]y = -3x + 4[/tex]
[tex]3x = 4-y[/tex]
[tex]x = \frac{4 - y}{3}[/tex]
The domain of x is the real numbers, which means that for each value of y, there is a value of x such that [tex]f(x) = y[/tex]. So, the function is surjective.
A function f(x) is bijective when it is both injective and surjective. So this function is bijective.
