Consider the three functions on suitable subsets of :

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Consider the three functions on suitable subsets of

\mathbb{R}

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

(i) Form the function

F(x)=2f(x)-3g(x)+h(x)

and simplify the expression as far as possible. (ii) Determine the domain of

F(x)