For this case we have the following functions:
[tex]f (x) = 4x + 7\\g (x) = 3x-5[/tex]
We must find [tex](g_ {o} f) (x).[/tex] By definition of composition of functions we have to:
[tex](g_ {o} f) (x) = g (f (x))[/tex]
So:
[tex]g (f (x)) = 3 (4x + 7) -5\\g (f (x)) = 12x + 21-5\\g (f (x)) = 12x + 16[/tex]
Finally we have to:
[tex](g_ {o} f) (x) = 12x + 16[/tex]
We evaluate at [tex]x = -4:[/tex]
[tex](g_ {o} f) (- 4) = 12 (-4) + 16 = -48 + 16 = -32[/tex]
Answer:
[tex]-32[/tex]
