Question

What is (f−g)(x)? f(x)=5x^4+4x^3+3x^2+2x+1 g(x)=x^4+2x^3+3x^2+4x+5. Enter your answer, in standard form, in the box.

Answer 1

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

Explanation:

Let f and g be two functions that are defined in the same interval and have the same independent variable. Then, the Subtraction of Function is defined as:

`(f-g)(x)=f(x)-g(x)`

Let's solve (f-g)(x) with
`f(x)=5x^(4)+4x^3}+3x^(2)+2x+1` and
`g(x)=x^(4)+2x^(3)+3x^(2)+4x+5`

`(f-g)(x)=(5x^(4)+4x^3}+3x^(2)+2x+1)-(x^(4)+2x^(3)+3x^(2)+4x+5)\\(f-g)(x)=5x^(4)+4x^3}+3x^(2)+2x+1-x^(4)-2x^(3)-3x^(2)-4x-5\\(f-g)(x)=4x^(4)+2x^3}-2x-4`

.