Final answer:
To find an integer value for c such that g(x) = 1/(3x - c) is different from f(x) = 1/(3x), c should not be 3. Therefore, the possible correct answers are c = 1, c = 2, and c = 4.
Step-by-step explanation:
The student's question revolves around finding an integer value for c such that the function g(x) = 1/(3x - c) is defined. Given the options A) c = 1, B) c = 2, C) c = 3, and D) c = 4, we want to identify a value of c such that g(x) is a valid function and is different from the function f(x) = 1/(3x).
To ensure that g(x) is different from f(x), we need to choose a c value that changes the denominator in a way that it does not simplify to 3x. If c were 3, then the denominator of g(x) would become 3x - 3 = 3(x - 1), which could simplify to a similar form as f(x) after factoring out the 3. Therefore, to keep the functions distinct, c should not be 3, leaving us with the options A) c = 1, B) c = 2, and D) c = 4 as potential correct answers.