Question

What is the additive inverse of -6x2+x-2

Answer 1

Additive inverse is
`g(x)=6x^(2)-x+2`

Explanation:

We have the function
`f(x)=-6x^(2)+x-2`.

Now, for the additive inverse, we have the property that, there exists a function g(x) such that f(x)+g(x) = g(x)+f(x) = 0.

So, we have,

f(x)+g(x) = g(x)+f(x) = 0

i.e.
`(-6x^(2)+x-2)+g(x)=g(x)+(-6x^(2)+x-2)=0`

i.e.
`(-6x^(2)+x-2)+g(x)=0` and
`g(x)+(-6x^(2)+x-2)=0`

i.e.
`g(x)=6x^(2)-x+2` and
`g(x)=6x^(2)-x+2`

i.e.
`g(x)=6x^(2)-x+2`

Thus, the additive inverse of
`f(x)=-6x^(2)+x-2` is
`g(x)=6x^(2)-x+2`.

Answer 2

The additive inverse is
`A=6x^2-x+2`

Explanation:

The given expression is

`-6x^2+x-2`

Let the additive inverse of given expression be A.

The sum of a term and its additive inverse is 0.

If,

`a+(-a)=0`

Then additive inverse of a is -a.

`(-6x^2+x-2)+A=0`

`A=6x^2-x+2`

Therefore the additive inverse is
`A=6x^2-x+2`.