The function f is defined by f(c) = 1/(x - 2) - 1/x where x ≠ 2 and x ≠ 0. If f(c) = 1/12, which of the following could be the value of c?.
Indicate all such values.

Rationale

c could be -4 or 6.

To solve for c in the equation f(c) = 1/(x - 2) - 1/x = 1/12, we need to find values of x that satisfy this function. After simplifying the equation, we can determine that both c = -4 and c = 6 yield valid results.

A (-12) YOUR ANSWER

Substituting c = -12 into the function results in f(-12) = 1/(-12 - 2) - 1/(-12). This simplifies to f(-12) = 1/(-14) + 1/12, which does not equal 1/12. Therefore, -12 is not a valid solution.

B (-6) YOUR ANSWER

For c = -6, we calculate f(-6) = 1/(-6 - 2) - 1/(-6). This gives f(-6) = 1/(-8) + 1/6. After calculating, this does not equal 1/12, thus -6 is not a valid solution.

C (-4) CORRECT

Plugging c = -4 into the function, we find f(-4) = 1/(-4 - 2) - 1/(-4). This simplifies to f(-4) = 1/(-6) + 1/4. Which equals 1/12 after finding a common denominator. Therefore, -4 is a valid solution.

D (4) YOUR ANSWER

Substituting c = 4 gives f(4) = 1/(4 - 2) - 1/4, resulting in f(4) = 1/2 - 1/4 = 1/4, which does not equal 1/12. Hence, 4 is not a valid solution.

E (6) CORRECT

For c = 6, we compute f(6) = 1/(6 - 2) - 1/6, resulting in f(6) = 1/4 - 1/6. This simplifies to 1/12, confirming that 6 is a valid solution.

Conclusion

To determine which values of c make the function equal to 1/12, we found valid solutions at c = -4 and c = 6. The other choices did not satisfy the equation, confirming that only these two values meet the criteria set by the function definition.

The function f is defined by f(c) = 1/(x - 2) - 1/x where x ≠ 2 and x ≠ 0. If f(c) = 1/12, which of the following could be the value of c?. Indicate all such values.

c could be -4 or 6.

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The function f is defined by f(c) = 1/(x - 2) - 1/x where x ≠ 2 and x ≠ 0. If f(c) = 1/12, which of the following could be the value of c?.
Indicate all such values.