The functions fff and ggg are defined by
f(x)=12−3xfor x≤4 f(x) = \sqrt{12 - 3x} \quad \text{for } x \le 4 f(x)=12−3xfor x≤4 g(x)=1xfor x≠0 g(x) = \frac{1}{x} \quad \text{for } x \ne 0 g(x)=x1for x=0The 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.
