hela9astrid
hela9astrid hela9astrid
  • 24-03-2020
  • Mathematics
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shilpa85475 shilpa85475
  • 30-03-2020

f(g(11)) = -6

Solution:

Given data:

[tex]f(x)=x^{2}-6 x+3[/tex]

[tex]g(x)=\sqrt{x-2}[/tex]

To find f(g(11)):

Substitute x = 11 in g(x).

[tex]g(11)=\sqrt{11-2}[/tex]

        [tex]=\sqrt{9}[/tex]

[tex]g(11)=3[/tex]

Substitute g(11) = 3 in f(g(11)).

[tex]f(g(11))=f(3)[/tex]

[tex]f(x)=x^{2}-6 x+3[/tex]

[tex]f(3)=3^{2}-6 (3)+3[/tex]

[tex]f(3)=9-18+3[/tex]

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

[tex]f(g(11))=f(3)[/tex]

             = -6

Hence f(g(11)) = -6.

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