1) Given that the functions f(x) = cos x and g(x) = sin x, which operations can be used to combine the two functions to create a new function with an amplitude that is less than 1? (1m) 2) Is the difference of two odd functions odd or even? Justify your answer with two examples. (2m) 3) Express the volume of a sphere of radius ' r ' as a function of (4m) a) the circumference b) the surface area 4) Let f(x) = { ( -9, -2 ), (-6, -3), (-3, 0), (0, 2), (3, 7) } and g(x) = { (-12, 9), (-9, 4), (-8, 1), (-7, 10), (-6, -6), (0, 12)} . Determine (8m) a) ( f + g ) (x) b) ( g + f ) (x) c) ( f - g) (x) d) (g - f ) (x) 5) Determine (f g) (x) for each of the following pairs of functions, and state its domain (6m) a) f (x ) = 1 2 g (x) = + 1 2 b) f(x) = 10 g(x) = sin (3x) c) f(x) = 11 x3 g(x) = + 6) A pendulum is released and