math
posted by Nicholas Lim on .
Given f(x)=23x and g(x)=hx+k where h and k are constants.If gf(1)=6 and g^1(4)=g(4),find the possible values of h and k?

First write expressions for gf(x) and g^1(x) in terms of h and k.
Then write equations for gf(1) and g^(1)(4)
This will leave you with two equations that involve only h and k.
Solve them simultaneously.
For starters,
gf(x) = h(23x) + k = 2h 3hx + k
gf(1) = 2h + 3h + k = 5h + k
Now compute the inverse function of g and complete the solution.
See if you get
g^1(x) = [(xk)/h] + k