Answer:
p = 2, q = 14
Explanation:
Evaluate f(g(x)) and compare to 6x + q
To evaluate f(g(x)) substitute x = g(x) into f(x), that is
f(g(x))
= f(px + 4)
= 3(px + 4) +p ← distribute and simplify
= 3px + 12 + p
Now f(g(x)) = 6x + q
Comparing like terms between the 2 expressions
3px = 6x, that is
3p = 6 ( divide both sides by 3 )
p = 2
And
q = 12 + p = 12 + 2 = 14