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Advanced Math / Nonlinear functions Difficulty: Easy

f of x equals, open parenthesis, x plus 0 point 2 5 x, close parenthesis, times, open parenthesis, 50 minus x, close parenthesis

The function f is defined above. What is the value of f of 20 ?

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Explanation

Choice C is correct. Adding the like terms x and 0 point 2 5 x yields the equation f of x equals, 1 point 2 5 x times, open parenthesis, 50 minus x, close parenthesis. Substituting 20 for x yields f of 20 equals, open parenthesis, 1 point 2 5 times 20, close parenthesis, times, open parenthesis, 50 minus 20, close parenthesis. The product 1 point 2 5 times 20 is equal to 25, and the difference 50 minus 20 is equal to 30. Substituting these values in the given equation gives f of 20 equals, 25 times 30, and multiplying 25 by 30 results in f of 20 equals 750.

Choices A, B, and D are incorrect and may result from conceptual or computational errors when finding the value of f of 20.