The function f f\,f is defined by f(x)=(x−2)2−9f(x) = (x - 2)^2 - 9f(x)=(x−2)2−9 for x≥kx \geq kx≥k, where k k\,k is a constant. For parts (b) to (d), use the least possible value of k k\,k found in part (a).
Given that f−1(x)f^{-1}(x)f−1(x) exists, state the least possible value of kkk.
Evaluate ff(6)ff(6)ff(6)
Solve the equation f(x)=xf(x) = xf(x)=x
Explain why your answer to part (c) is also the solution to the equation f(x)=f−1(x)f(x) = f^{-1}(x)f(x)=f−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.