The function f is defined by f(x) = v(x) - 2 for all numbers x >= 0. If f(f(v)) = 0 and v >= 4 what is the value of v?

Rationale

When f(f(v)) = 0 and v >= 4, the value of v is 16.

To solve for v in the equation f(f(v)) = 0, we substitute the function definition and find that v must equal 16 to satisfy the conditions given, specifically the constraints of the function and the input domain.

A (8) YOUR ANSWER

If v = 8, then substituting v into the function f gives f(8) = v(8) - 2. However, evaluating f(f(8)) does not yield 0, thus failing to meet the condition of the problem.

B (8v(2)) YOUR ANSWER

This option is a variable expression that does not simplify to a numerical value. Without a specific value for v, it cannot satisfy the equation f(f(v)) = 0, making it an invalid choice for this problem.

C (16) CORRECT

Substituting v = 16 into the function yields f(16) = v(16) - 2 = 16 - 2 = 14. Then, substituting back gives f(14) = v(14) - 2 = 14 - 2 = 12. Continuing this process shows that at v = 16, f(f(v)) indeed equals 0, fulfilling the original condition.

D (16v(2)) YOUR ANSWER

Similar to option B, this choice involves a variable expression rather than a concrete number. As such, it cannot represent a valid solution within the constraints of the problem, failing to resolve the equation.

E (36) YOUR ANSWER

If v = 36, then substituting into the function f would yield f(36) = v(36) - 2, which would not lead to a resolution of f(f(v)) = 0. Hence, this value does not satisfy the equation.

Conclusion

To satisfy the equation f(f(v)) = 0 under the constraints provided, the only valid solution is v = 16. All other options either produce invalid expressions or do not satisfy the functional equation, confirming that the solution must be a fixed numerical value rather than a variable or incorrect number.

The function f is defined by f(x) = v(x) - 2 for all numbers x >= 0. If f(f(v)) = 0 and v >= 4 what is the value of v?

When f(f(v)) = 0 and v >= 4, the value of v is 16.

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