Respuesta :

absor201

Answer:

Part 1):

  • [tex]f(g(6))=19[/tex]

Part 2):

  • [tex]g(f(-7))=-34[/tex]

Part 3):

  • [tex]f(f(8))=224[/tex]

Part 4):

  • [tex]g(f(x))=5x+1[/tex]

Step-by-step explanation:

Considering the function

[tex]f(x) = 5x + 4[/tex]

[tex]g(x) = x - 3[/tex]

Part 1)

To evaluate [tex]f(g(6))[/tex], you must find [tex]g(6)[/tex]

so

[tex]g(x) = x - 3[/tex]

Put x = 6

[tex]g(6) = 6 - 3[/tex]

[tex]g(6) = 3[/tex]

Then  

[tex]f(g(6))=f(3)[/tex]

[tex]=5(3)+4[/tex]

[tex]=19[/tex]

Therefore, [tex]f(g(6))=19[/tex]

Part 2)

To evaluate [tex]g(f(-7))[/tex], you must find [tex]f(-7)[/tex]

so

[tex]f(x) = 5x + 4[/tex]

Put x = -7

[tex]f(-7) = 5(-7) + 4[/tex]

[tex]=-35+4[/tex]

[tex]=-31[/tex]

Then  

[tex]g(f(-7))=g(-31)[/tex]

[tex]= (-31) - 3[/tex]

[tex]=-34[/tex]

Therefore, [tex]g(f(-7))=-34[/tex]

Part 3)

To evaluate [tex]f(f(8))[/tex], you must find [tex]f(8)[/tex]

[tex]f(x) = 5x + 4[/tex]

Put x = 8

[tex]f(8)=5(8)+4=40+4=44[/tex]

Then

[tex]f(f(8))=f(44)=5(44)+4=220+4=224[/tex]

Therefore,

[tex]f(f(8))=224[/tex]

Part 4)

Evaluate

[tex]g(f(x))[/tex]

As

[tex]f(x) = 5x + 4[/tex]

[tex]g(x) = x - 3[/tex]

so

[tex]g(f(x))=g(5x+4)[/tex]

            [tex]=(5x+4)-3[/tex]

            [tex]=5x+4-3[/tex]

            [tex]=5x+1[/tex]

Therefore,

[tex]g(f(x))=5x+1[/tex]