Find a non-constant function f(x) such that its average value over the interval [1,6] is 1

Question

Is there a formula or method to solve this that is fast and easy? The only way I can think to solve this is to guess and check but that is going to take awhile.

Answer 1

Linear functions are very easy to use here - the average of a linear function on an interval is its value at the midpoint of the interval. So all we have to do here is pick a linear function that has a value of 1 at x = 4.

Something like y = x / 4 would work, or alternately y = x - 3.