Calculus :Tutorial 1

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Calculus :Tutorial 1

  1. 1. PMB 3004: Calculus Tutorial 11. Which of the following illustrates a function?                   (a) (c)               2. State whether the following graphs represent functions or not. Give reasons for your answers. y y 0 x 0 x y y 0 x 0 x
  2. 2. y 0 x3. If f : x  2 x  3 , what is the image of 6 ? Find the values of f (6) , f (1) , f (0) , 5 f (12) .4. If f ( x)  2 x  3 and g ( x)  x 2  5 , find the following: (a) gf (2) ; (b) fg (3) ; (c) fg (a  1) ; (d) gf ( x  1) .5. If f : x  2 x , g : x  x  1 and h : x  x , build up formulae for the composite 2 functions fgh , hfg , gfh and hgf .6. Find the inverse functions for each of the following: (a) f : x  x  4 ; (b) g : x  3x  1 ; (c) h : t  12 - 7 4 t7. Given that f : x  x , find the value(s) of x for which f 1 ( x)  f ( x) . 2x  38. Find f if g and gf are given as follows: (a) g(x) = 2/x , x ≠ 0 and gf(x) = 2/(x-1), x ≠ 1 (b) g(x) = x-2 and gf(x) = 3x-79. Find g if f and gf are given as follows: (a) f(x) = 4x , x ≠ 0 and gf(x) = 4x-3 (b) f(x) = 2x-1 and gf(x) = 6x-3

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