Respuesta :

absor201

Answer:

  • [tex]f(g(6))=19[/tex]
  • [tex]g(f(-7))=-34[/tex]
  • [tex]f(f(8))=224[/tex]
  • [tex]g(f(x))=5x+1[/tex]

Step-by-step explanation:

Considering the functions

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

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

Part 1)

Find

  • [tex]f(g(6))[/tex]

We need to first dertermine [tex]g(6)[/tex]

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

Putting x = 6

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

Then

[tex]f(g(6))=f(3)=5(3)+4=15+4=19[/tex]

Hence,

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

Part 2)

Find

  • [tex]g(f(-7))[/tex]

We need to first dertermine [tex]f(-7)[/tex]

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

Putting x = -7

[tex]f(-7) = 5(-7)+4=-35+4=-31[/tex]

Then

[tex]g(f(-7))=g(-31)=(-31-3)=-34[/tex]

Hence,

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

Part 3)

Find

  • [tex]f(f(8))[/tex]

We need to first dertermine [tex]f(8)[/tex]

Putting 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]

Hence,

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

Part 4)

Find

  • [tex]g(f(x))[/tex]

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

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

         [tex]=(5x+4)-3=5x+1[/tex]

Hence,

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

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