A manufacturer models the production cost CCC (in thousands of dollars) of a specialty polymer as a function of the weight www (in tons) produced, defined by:
C(w)=15(w2+6),w≥0 C(w) = \frac{1}{5}(w^2 + 6), \quad w \ge 0 C(w)=51(w2+6),w≥0Determine the range of the cost function CCC.
Find an expression for the inverse function C−1(x)C^{-1}(x)C−1(x).
State the range of C−1(x)C^{-1}(x)C−1(x).
State the geometric transformation that maps the graph of y=C(w)y = C(w)y=C(w) onto the graph of y=C−1(w)y = C^{-1}(w)y=C−1(w).
Find the coordinates of the points of intersection of the graphs of y=C(x)y = C(x)y=C(x) and y=C−1(x)y = C^{-1}(x)y=C−1(x).
532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, 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). Each one has a worked solution and a mark scheme showing where the marks go.