Final answer:
To find the value of 'a' for which f(x) = x/(x + a) is a self-inverse function, we solve the equation f(f(x)) = x.
Step-by-step explanation:
To find the value of 'a' for which f(x) = x/(x + a) is a self-inverse function, we need to solve f(f(x)) = x.
Substituting f(x) into the equation f(f(x)) = x, we get f(f(x)) = x/(x + a) = x.
To solve this equation, we multiply both sides by (x + a) to eliminate the denominator, giving us x = x(x + a).
Expanding and rearranging this equation, we get x^2 + ax - x = 0.
Finally, we can solve this quadratic equation to find the value of 'a' that makes f(x) a self-inverse function.