Final answer:
To find the linear function f(x), we can use the given information and the properties of linear functions. By using the information f(5) = 8 and the inverse property equation, we can determine the slope and y-intercept of the linear function. Finally, we can form the equation f(x) = mx + b to express the linear function.
Step-by-step explanation:
To find the linear function f(x), let's first use the information given. We know that f(5) = 8, which means when x = 5, f(x) = 8. Since f(x) is a linear function, we can represent it as f(x) = mx + b, where m is the slope and b is the y-intercept.
So, we have the equation 8 = 5m + b. Now, to find the slope, we can use the inverse property given in the question. f^-1(x) - f^-1(x-2) = 1/4 gives us the relationship between the inverse function of f(x) and the inverse function of f(x-2).
Based on the given information, let's assume f^-1(y) = ax + c. Substituting this into the inverse property equation, we get ax - (a(x-2) + c) = 1/4. Simplifying this equation, we find that a = -1/4.
Now, we can substitute the values for m and b into the equation 8 = 5m + b and solve for b. Plugging in m = -1/4, we get 8 = 5(-1/4) + b. Solving this equation, we find that b = 9. Therefore, the linear function f(x) is f(x) = -1/4x + 9.
Learn more about Finding a linear function given specific information