Theory question 102
Functions(a) Two functions p and q are defined on the set of real numbers, R, by p: y → 2y + 3 and q: y → y2 − 2. Find q o p
(b) How many four digits odd numbers greater than 4000 can be formed from 1, 7, 3, 8, 2 if repetition is allowed?
Show the model answer
Model answer
(a) q o p(y) = q(2y + 3) = (2y + 3)² − 2 = 4y² + 12y + 7.
(b) First digit 7 or 8 (2 ways, to exceed 4000); second and third digits any of 5; last digit 1, 7 or 3 (3 ways).
2 × 5 × 5 × 3 = 150.
Explanation
Fill the restricted places (first and last) first.