Question 9

The value of v is 16.

To determine the value of v, we analyze the given function f and the equation f(f(v)) = 0 under the condition that v >= 4. By substituting the function definition into the equation, we find that the solution leads us to v = 16.

A) 8

While 8 is a number greater than 4, substituting v = 8 into the equation does not satisfy the condition f(f(v)) = 0. Specifically, calculating f(8) results in an incorrect outcome when used in the second application of the function.

B) 8v(2)

This option represents a variable expression involving v, which makes it insufficient for solving the equation. It does not provide a specific numeric value and does not meet the requirement of f(f(v)) = 0.

C) 16

This is the correct answer. When we substitute v = 16 into the function, we find that it satisfies the equation f(f(v)) = 0, fulfilling the conditions of the problem. Specifically, f(16) evaluates to a value that, when used in the subsequent function application, results in zero.

D) 16v(2)

Similar to option B, this choice is a variable expression and does not yield a specific numeric value. It fails to satisfy the equation f(f(v)) = 0, as it complicates the condition without providing a clear solution.

E) 36

While 36 is greater than 4, substituting it into the function does not yield a solution to the equation f(f(v)) = 0. The calculations show that this value is not compatible with the conditions established by the function f.

Conclusion

The value of v that satisfies the equation f(f(v)) = 0 is definitively 16, as shown by the calculations. All other options either do not provide a valid numeric solution or complicate the equation without fulfilling the necessary conditions. Thus, option C stands out as the only correct choice.