PMB 3004: Calculus

Tutorial 1

1. 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

x0

y

x0

y

x0

y

x0

y

x0

3. If 5

32: xxf , what is the image of 6 ? Find the values of )6(f , )1(f , )0(f ,

)12(f .

4. If 32)( xxf and 5)( 2 xxg , find the following:

(a) )2(gf ; (b) )3(fg ; (c) )1( afg ; (d) )1( xgf .

5. If xxf 2: , 1: xxg and 2

: xxh , build up formulae for the composite

functions fgh , hfg , gfh and hgf .

6. Find the inverse functions for each of the following:

(a) 4: xxf ; (b) 4

13: xxg ; (c) t

th 12: - 7

7. Given that 32

:xxxf , find the value(s) of x for which )()(1 xfxf .

8. 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-7

9. 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