The function fff is defined by
f(x)=4x−1x−3,x>3 f(x) = \frac{4x - 1}{x - 3}, \quad x > 3 f(x)=x−34x−1,x>3Show, by using calculus, that fff is a decreasing function.
Find f−1(x)f^{-1}(x)f−1(x).
(i) Show that ff(x)=ax+bx+cff(x) = \frac{ax + b}{x + c}ff(x)=x+cax+b where a,b,a, b,a,b, and ccc are constants to be found. (ii) Deduce the range of ffffff.
