Page 04 MARKS 5. Find ∫ ( ) 8cos 4 1 + x dx. 6. Functions f and g are defined on , the set of real numbers. The inverse functions f −1 and g−1 both exist. (a) Given ( ) 3 5 = + f x x , find ( ) 1 − f x . (b) If g ( ) 2 = 7, write down the value of g−1 ( ) 7 . 7. Three vectors can be expressed as follows: FG = −2i −6j + 3k GH = 3i + 9j −7k EH = 2i + 3j + k (a) Find FH. (b) Hence, or otherwise, find FE. 8. Show that the line with equation = 3 5 − y x is a tangent to the circle with equation 2 2 2 4 5 0 + + − − = x y x y and find the coordinates of the point of contact. 2 3 1 2 2 5