Question

the cost of producing x soccer balls in thousands of dollars is represented by \\(h(x) = 5x + 6\\). the revenue is represented by \\(k(x) = 9x - 2\\). which expression represents the profit, \\((k - h)(x)\\), of producing soccer balls?

\\(14x - 8\\)
\\(14x + 4\\)
\\(4x - 8\\)
\\(4x + 4\\)

Explanation:

Set up the function subtraction expression

$$ (k - h)(x) = k(x) - h(x) $$

Substitute the given function formulas

$$ (k - h)(x) = (9x - 2) - (5x + 6) $$

Simplify the polynomial expression

$$ (k - h)(x) = 9x - 2 - 5x - 6 = 4x - 8 $$

Answer:

• (A) \(14x - 8\)
• (B) \(14x + 4\)
• (C) \(4x - 8\) (Correct answer)
• (D) \(4x + 4\)