Questions marked * are to be handed directly to tutors by the end of the second tutorial

1. Stewart p.414: 11, 13, 15, 17 ( p.350: 7, 9, 11)

2. Stewart p.415: 23, 25, 27, 33 (p.351: 13, 15, 17)

3. Stewart p. 415: 35, 37, 43 (p.351: 19, 21, 23)

*4. Show that f(x) = x³ + x is 1 – 1 by three methods (a) graphically (b) calculus (c) algebra

(Hint: for (c) you may need the identity x² + xy + y² = (x + y/2)² + 3/4y² ).

*5. If f(x) = x/(x-1)and g(x) = x² +1, find (fog)(x) and (gof)(x) and their domain and range.

*6. If f(x) = (x-1)/(x+1), find f ^-1(x) and the domain and range of f and f ^-1 and sketch them on the

same graph.