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>4 C(x) = \frac{5x - 2}{x - 4}, \quad x > 4 C(x)=x−45x−2,x>4Use 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 AQA A Level Maths 1.5 B: Algebra and functions with exam-style questions for A Level Maths. 358 questions covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only), matched to the AQA A Level Maths (7357) 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.
