Question

Cynthia was offered two different jobs for the summer. working as a camp counselor, she will earn $15 per hour plus an additional $25 bonus. her earnings after x hours can be represented by the function f(x) = 15x 25. working as a lifeguard, cynthia will earn $10 per hour and an additional $50 bonus. her earnings after x hours can be represented by the function g(x) = 10x 50. the arithmetic operation (f − g)x can be used to determine the difference in the salary cynthia will earn working as a camp counselor instead of a lifeguard after x hours. what is the function (f − g)x? (f − g)x = 5x − 25 (f − g)x = 5x 75 (f − g)x = 25x 75 (f − g)x = 25x − 25

Answer 1

The value of the composite function (f - g)(x) is 5x - 25

How to determine the function (f - g)(x)?

The function definitions are given as:

f(x) = 15x + 25

g(x) = 10x + 50

The function (f - g)(x) is calculated using

(f - g)(x) = f(x) - g(x)

This gives

(f - g)(x) = 15x + 25 - 10x - 50

Evaluate the like terms

(f - g)(x) = 5x - 25

Hence, the value of the composite function (f - g)(x) is 5x - 25

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Complete question

Cynthia was offered two different jobs for the summer. working as a camp counselor, she will earn $15 per hour plus an additional $25 bonus. her earnings after x hours can be represented by the function f(x) = 15x + 25. working as a lifeguard, Cynthia will earn $10 per hour and an additional $50 bonus. her earnings after x hours can be represented by the function g(x) = 10x + 50. the arithmetic operation (f - g)x can be used to determine the difference in the salary Cynthia will earn working as a camp counselor instead of a lifeguard after x hours. what is the function (f - g)x?