Mathematics

Problem

Let the functions

f

g

and

h

be defined by

f(x)=\sqrt{4-x}, \; g(x)=\dfrac{x^{2}-9}{x-3}, \; h(x)=\dfrac{1}{x+1}

, wherever they are meaningfully defined. a. (i) Write the expression

P(x)=\dfrac{f(x)\, g(x)}{h(x)}-g(x)

and simplify it completely. b. (ii) Find the domain of

P(x)

, clearly indicating every step that leads to the final answer.