Final Answer:
f(4) = 3 / (2√143).
Step-by-step explanation:
To find f(4) for the given function f(x) = 6 / sec^(-1)(3x), we substitute x = 4 into the expression. The expression becomes 6 / sec^(-1)(3 * 4). We then simplify this by evaluating sec^(-1)(12) and express the result in the given format, yielding 3 / (2√143).
In summary, to find f(4), we substitute the value of x into the function and perform the necessary calculations. The final answer 3 / (2√143) represents the value of the function at x = 4. Understanding the trigonometric functions and their inverses is crucial for evaluating expressions involving inverse trigonometric functions.
It's important to note that the result 3 / (2√143) is obtained through the proper evaluation of the given expression, demonstrating the application of trigonometric concepts and algebraic manipulations to arrive at the desired solution.