2020 WAEC Further Mathematics Theory (a) Two functions p and q are defined on the set of real numbers, R,...

(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?

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

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