Computers and Technology, 14.09.2019 09:10 Dallas6797

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

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Answer from: wereallmadhere111

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:

f(x) = -3x + 4

f(a) = f(b)

-3a + 4 = -3b + 4

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

3a = 3b

$a = \frac{3b}{3}$

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

$x = \frac{4 - y}{3}$

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.

Answer from: Quest

whats

Answer from: Quest

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