Question

refer to the functions r and p. find the function ((r - p)(x)) and write the domain in interval notation.
(r(x) = -4x)
(p(x) = x^2 + 7x)
(q(x) = sqrt{5 - x})

part: 0 / 2

part 1 of 2

((r - p)(x) = square)

Explanation:

Step1: Recall the definition of function subtraction

The formula for \((r - p)(x)\) is \(r(x)-p(x)\).

Step2: Substitute the given functions

We know that \(r(x)=-4x\) and \(p(x)=x^{2}+7x\). So, \((r - p)(x)=r(x)-p(x)=-4x-(x^{2}+7x)\).

Step3: Simplify the expression

First, distribute the negative sign: \(-4x - x^{2}-7x\). Then, combine like terms: \(-x^{2}+(-4x - 7x)=-x^{2}-11x\).

Answer:

\(-x^{2}-11x\)