An environmental study models the concentration of a chemical byproduct, CCC, in mg/L, as a function of the distance xxx, in km, from the source of the spill. The concentration is given by the function: C(x)=5x−2x−4,x>4C(x) = \frac{5x - 2}{x - 4}, \quad x > 4C(x)=x−45x−2,x>4
Use calculus to prove that CCC is a decreasing function for its entire domain.
Find an expression for the inverse function C−1(x)C^{-1}(x)C−1(x).
Show that the composite function C(C(x))=ax+bx+cC(C(x)) = \frac{ax + b}{x + c}C(C(x))=x+cax+b where a,b,a, b,a,b, and ccc are constants to be determined.
Deduce the range of C(C(x))C(C(x))C(C(x)).
Practise Edexcel A Level Maths 2.4 Inverse Functions with exam-style questions for A Level Maths. 41 questions, 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.