Question 1.

Consider the functions given below.

f(x) = 2x + 3 g(x) = 1/x, x ≠ 0

(a)   (i) Find (g ○ f)(x) and write down the domain of the function.

(ii)      Find (f ○ g)(x) and write down the domain of the function.                       (2)   (b)      Find the coordinates of the point where the graph of y = f(x) and the graph of y = (g–1 ○ f ○ g)(x) intersect.                                                                               (4)                                                                                                            (Total 6 marks) Quesstion 2. The diagram below shows the graph of the function y = f(x), defined for all x  , where b > a > 0. Consider the function g(x) = . $$f(x)=x^2+2x+1$$ $$y=x^3$$