(a) Two functions p and q are defined on the set of real numbers, R, by p : y \(\to\) 2y +3 and q : y -> y – 2. Find QOP
(b) How many four digits odd numbers greater than 4000 can be formed from 1,7,3,8,2 if repetition is allowed?
Explanation
P(y) = 2y + 3, q(y) = y\(^2\) - 2
q \(\cap\) p = qp(y)
= q(2y + 3)
= (2y + 3)\(^3\) - 2
= 4xy\(^2\) + 12y + 9 - 2
= 4y\(^2\) + 12y + 7
(b)
No. of ways = 2 x 5 x 5 x 5
= 250 ways