Question

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

Answer 1

Answer:

Additive inverse is $g(x)=6x^{2}-x+2$

Step-by-step 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

Answer:

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

Step-by-step 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 $A=6x^2-x+2$.