Question

Given f(x)=2-3x 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?

Answer 1

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(2-3x) + 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) = [(x-k)/h] + k