g = 3×+5/4 and f= 4×+3 determine what is gf(×)

Answer 1

To determine g(f(x)) do the following:

1. take equation of g(x) which in this case is : 3x + 5 / 4
2. where there is x in the g(x) equation, put () in there, and inside of them write the equation of f(x), then solve that equation.

for example:

g(x) = 3x + 5/4

f(x) = 4x + 3

g(f(x)) = 3 (4x + 3) + 5/4

=> g(f(x)) = 12x + 9 + 5/4

=> g(f(x)) = 12x + 41/4

similarly:

f(g(x)) = 4 (3x + 5/4) +3

=> f(g(x)) = 12x + 20/4 + 3

=> f(g(x)) = 12x + 5 + 3

=> f(g(x)) = 12x + 8