The functions fff and ggg are defined by
f(x)=12−3xfor x≤4f(x) = \sqrt{12 - 3x} \quad \text{for } x \le 4f(x)=12−3xfor x≤4 g(x)=1xfor x≠0g(x) = \frac{1}{x} \quad \text{for } x \ne 0g(x)=x1for x=0
The function hhh has the maximum possible domain and is defined by h(x)=gf(x)h(x) = gf(x)h(x)=gf(x).
Find an expression for h(x)h(x)h(x).
Find the domain of hhh.
Show that h−1(x)=4−13x2h^{-1}(x) = 4 - \frac{1}{3x^2}h−1(x)=4−3x21.
Practise Edexcel A Level Maths Functions and Graphs with exam-style questions for A Level Maths. 100 questions 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, 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.