Question

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

Answer 1

The function is injective.

The function is surjective.

The function is bijective.

Step-by-step explanation:

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

So:

`f(x) = -3x + 4`

`f(a) = f(b)`

`-3a + 4 = -3b + 4`

`-3a = -3b` *(-1)

`3a = 3b`

`a = (3b)/(3)`

`a = b`

Since
`f(a) = f(b)` if, and only if,
`a = b`, 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:

`f(x) = y`

`y = -3x + 4`

`3x = 4-y`

`x = (4 - y)/(3)`

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

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