The function fff is defined by f(x)=4x−1x−3,x>3f(x) = \frac{4x - 1}{x - 3}, \quad x > 3f(x)=x−34x−1,x>3
Show, 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.
Practise Edexcel A Level Maths Functions and Graphs with exam-style questions for A Level Maths. 100 questions covering 2.1 The Modulus Function, 2.2 Functions and Mappings, 2.3 Composite Functions, 2.4 Inverse Functions, 2.5 y=|f(x)| and y=f(|x|), 2.6 Combining Transformations, and 2.7 Solving Modulus Problems, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.