Final answer:
The value of f(5) when f(x) = e^-(x-4) is approximately 0.3679.
Step-by-step explanation:
To find the value of f(5) when f(x) = e^-(x-4) and the function is defined for 4 < x < 6, simply substitute x with 5:
f(5) = e^-(5-4)
f(5) = e⁻¹
Since e⁻¹ is the inverse of the natural exponential function e, the value is approximately 0.3679 (rounded to four decimal places).
Therefore, f(5) is approximately 0.3679. This process demonstrates the evaluation of exponential functions within specified ranges, offering insights into function behavior and specific values at distinct points, valuable in mathematical analysis and various scientific and computational contexts.