Question

Ifq(r) = 3r + 1 andp(z) = x-1/3what is (q. p)(x)?

Answer 1

Given the functons;

q(r) = 3r + 1

p(z) = z-1/3

Required

what is (q. p)(z)?​

This is a composite function which can also be expressed as;

q(p(z))

q(p(z)) = q((z-1)/3)

To get q((z-1)/3), we will replace r in q(r) with (z-1)/3

q((z-1)/3) = 3((z-1)/3)+1

q((z-1)/3) = z-1 + 1

q((z-1)/3) = z

Hence the composite function(q. p)(z)​ is z