Question

Suppose that the functions r and s are defined for all real numbers x as follows R(x)=x+3 S(x)=4x+1 Write the expressions for (r+s)(x) and r•s)(x) and evaluate (r-s)(3)

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(Solution)

(r-s)(3) = -2

(Step-by-Step)

R(x) = x + 3 \quad \text{and} \quad S(x) = 4x + 1

(r+s)(x) = R(x) + S(x) = (x + 3) + (4x + 1) = 5x + 4

(r \cdot s)(x) = R(x) \cdot S(x) = (x + 3)(4x + 1) = 4x^2 + x + 12x + 3 = 4x^2 + 13x + 3

\text{To evaluate } (r-s)(3):

(r-s)(x) = R(x) - S(x) = (x + 3) - (4x + 1) = x + 3 - 4x - 1 = -3x + 2

(r-s)(3) = -3(3) + 2 = -9 + 2 = -7

(Step-by-Step)

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