Two functions f(x) and g(x) are defined on the set of real numbers by f(x) = 3�
2 − 2, and g(x) = x+3. Find : (i) f(-2)
(ii) �
−1( − 2);
(iii) the value of x for which f[g(x)] = g[f(x)]
(iv) �
−1
[� 4 ]
2. Given that p =2i +3j ,q = i+j ,r = i -2j. Find : (a) /2p-3q+r/
(b) the unit vector in the opposite direction of 2p-3q+ r
(c) the angle between p and r correct to the nearest degree
3. The data below shows the masses (in kg) at birth of forty babies born at a
maternity home I a week. 3.2 3.0 3.8 4.2 2.8 3.6 2.8 3.5
4.6 4.3 3.4 3.5 3.4 2.7 4.6 3.9
2.9 3.7 4.3 3.7 3.1 3.0 3.4 2.8
3.7 3.3 3.3 2.7 3.7 4.4 3.1 3.4
2.9 3.8 4.0 2.8 3.6 3.3 3.0 3.2
(a) Construct a frequency table using the class intervals: 2.25-2.75, 2.75-5.25, 3.25-3.75, 3.75-4.25 and 4.25-4.75kg
(b) Estimate :
(i) the median of the distribution
(ii) the mode of the distribution
(iii) the mean of the
