Respuesta :

Answer:

(f o g)(x)= 3x + 14

(g o f)(x) = 3x + 4

Step-by-step explanation:

(f o g)(x) = f(g(x)) = f(x + 5) = 3(x + 5) - 1 = 3x + 15 - 1 = 3x + 14

(g o f)(x) = g(f(x)) = g(3x - 1) = 3x - 1 + 5 = 3x + 4

chetankachana

Answer:

[tex](f \circ g)(x) = 3x + 14[/tex]

[tex](g \circ f)(x) = 3x + 4[/tex]

Step-by-step explanation:

Hello!

Rewrite the equations:

  • [tex](f \circ g)(x) = f(g(x))[/tex]
  • [tex](g \circ f)(x) = g(f(x))[/tex]

Given that:

  • f(x) = 3x - 1
  • g(x) = x + 5

Solve for [tex](f \circ g)(x)[/tex]:

  • [tex]f(g(x)) = 3(g(x)) - 1[/tex]
  • [tex]f(x + 5) = 3(x + 5) - 1[/tex]
  • [tex]f(x + 5) = 3x + 15 - 1[/tex]
  • [tex]f(x + 5) = 3x + 14[/tex]

[tex](f \circ g)(x) = 3x + 14[/tex]

Solve for [tex](g \circ f)(x)[/tex]:

  • [tex]g(f(x)) = f(x) + 5[/tex]
  • [tex]g(3x - 1) = (3x - 1) + 5[/tex]
  • [tex]g(3x - 1) = 3x +4[/tex]

[tex](g \circ f)(x) = 3x + 4[/tex]

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