hhhh85b
hhhh85b hhhh85b
  • 16-01-2020
  • Mathematics
contestada

Let f(x) = 4x + 7 and g(x) = 3x - 5. Find (gof)(-4).

Respuesta :

carlosego
carlosego carlosego
  • 28-01-2020

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]

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