Problem Set: A

(1) For the function f(x) =

x + 1/

x^{2 + 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 the expression.