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QuestionFind (p−r)(x)(p-r)(x) for r(x)=−4xr(x)=-4x and p(x)=x2+2xp(x)=x^2+2x. Determine the domain of (p−r)(x)(p-r)(x).

Studdy Solution

STEP 1

Assumptions1. The function r(x)=−4xr(x) = -4x . The function p(x)=x+xp(x) = x^ +x
3. We are asked to find the function (p−r)(x)(p-r)(x)

STEP 2

The function (p−r)(x)(p-r)(x) is defined as p(x)−r(x)p(x) - r(x). So, we need to subtract the function r(x)r(x) from the function p(x)p(x).
(p−r)(x)=p(x)−r(x) (p-r)(x) = p(x) - r(x)

STEP 3

Now, plug in the given functions p(x)p(x) and r(x)r(x).
(p−r)(x)=(x2+2x)−(−x) (p-r)(x) = (x^2 +2x) - (-x)

STEP 4

implify the expression by removing the parentheses. Remember that subtracting a negative is the same as adding a positive.
(p−r)(x)=x2+2x+4x (p-r)(x) = x^2 +2x +4x

STEP 5

Combine like terms to simplify the expression further.
(p−r)(x)=x2+x (p-r)(x) = x^2 +x So, the function (p−r)(x)(p-r)(x) is x2+xx^2 +x.

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