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).
471 exam-style questions on Edexcel A Level Maths Functions and Graphs, 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. Each one has a worked solution and a mark scheme showing where the marks go.