Final answer:
The inverse function of f(x) = 5/2x - 10 is f^(-1)(x) = (2/5)(x + 10).
Step-by-step explanation:
To find the inverse function in slope-intercept form, we can start by swapping the x and y variables, and then solve for y. So, the given function is y = 5/2x - 10. Swapping the variables, we get x = 5/2y - 10.
To solve for y, we can start by adding 10 to both sides of the equation to isolate the term with y. This gives us x + 10 = 5/2y. Then, we can multiply both sides by 2/5 to get y alone. This gives us y = (2/5)(x + 10).
So, the inverse function of f(x) = 5/2x - 10 is f^(-1)(x) = (2/5)(x + 10).