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.
