Find the difference of functions s and r shown below.
个
r(x) = -X? + 3x
s(x) = 2x + 1
(s - r)(x) =

x² - x + 1

Explanation:

Given:

r(x) = -x² + 3x

s(x) = 2x + 1

Required:

(s - r)(x)

Solution:

(s - r)(x) = s(x) - r(x)

Substitute

(s - r)(x) = (2x + 1) - (-x² + 3x)

Apply distribution property by multiply every term in the bracket by -1

(s - r)(x) = 2x + 1 + x² - 3x (recall: - × - = +; - × + = -)

Add like terms

(s - r)(x) = 2x - 3x + 1 + x²

(s - r)(x) = -x + 1 + x²

Rewrite in standard form

(s - r)(x) = x² - x + 1

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