Question

If f(x) = 4x^2+3x-5 and g(x)= -3x^2- 2x + 5, what is the value of (f-g)(x)?

Answer 1

`(f-g)(x)=7x^2+5x-10`

Explanation:

So we have the two functions:

`f(x)=4x^2+3x-5\text{ and } g(x)=-3x^2-2x+5`

And we want to find (f-g)(x).

This is the same thing to f(x)-g(x).

So, substitute:

`(f-g)(x)=f(x)-g(x)\\=(4x^2-3x-5)-(-3x^2-2x+5)`

Distribute the negative:

`=(4x^2+3x-5)+(3x^2+2x-5)`

Combine like terms:

`=(4x^2+3x^2)+(3x+2x)+(-5-5)`

Add or subtract:

`=7x^2+5x-10`

And we're done!

I hope this helps!