Question

Define g: Z->Z by f(x)=2x^2 +7x. Is f onto?Is f one-to-one?​

Answer 1

Answer:

The function is one-to-one

Step-by-step explanation:

f(x) = 2x^2 +7x

First we know this function is a parabola so it cannot be onto.

Since f(x)=1 does not exist

Now lets see if its one-to-one

Lets factor out x, and solve for roots

x(2x+7)

x = 0

2x + 7 = 0

2x = -7

x = -7/2

x = 0     ->  y = 0

x = -7/2 -> y = 0 ---> Not an integer, Z->Z

The reason I solved for the roots is to show that we have 2 x values that maps to 0, which will mean it cannot be a 1-1 function since in a 1-1 function each x has a unique y value, But if we take a look at the domain Z->Z this includes integer and -7/2 is not an integer so this function is one-to-one.