(1) For the function f(x) =
x + 1
x2 + 3 , evaluate and simplify the following:
(a) f(-1) (b) f(2a) (c) f(x2 + 3) (d) f (a
b - 1)
(2) State and use the appropriate formulae, find the sum of the odd numbers from 1 to 199,
inclusive.
(3) For the functions f(x) = 3x - 4 and g(x) = x + 2, find the following and determine
the domain in each case: (a) g((f)) (b) fg (c) f
g
(4) For the functions f(x) = √x - 3 and g(x) = √x + 2, find and determine the domain
in each case: (a) gf (b) f + g
(5) For the functions f(x) =
3
x - 4 and g(x) =
3 x
+ 4, find f(g(x)) and g(f(x)), hence or
otherwise determine whether g(x) is the inverse of f(x).
(6)
(a) Using the remainder theorem, determine whether (x - 4) and (x - 1) are factors
of the expression x3 + 3 x2 - 22 x - 24 .
(b) Hence, by use of long divison, find all remaining factors of t
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