Respuesta :

[tex]f(x)=\sqrt{x+7} \\ \\ \\ g(x)=8x-11 \\ \\ \\ (fog)(x)=\sqrt{(8x-11)+7} \\ \\ \\ = \sqrt{8x-4} \\ \\ \\ 2\sqrt{2x-1} \\ \\ \\ \\ \\ {GOOD \quad LUCK [/tex]

Answer:

fog(x) = [tex]2\sqrt{(2x - 1}[/tex].

Step-by-step explanation:

Given : f(x) = Square root of quantity x plus seven.; g(x) = 8x - 11 .

To find : Find f(g(x)).

Solution : We have given

f(x) = [tex]\sqrt{x+7}[/tex], g(x) = 8x - 11 .

fog(x) =  [tex]\sqrt{8x - 11+7}[/tex].

fog(x) =  [tex]\sqrt{8x - 4}[/tex].

Taking common 4

fog(x) =  [tex]\sqrt{4(2x - 1}[/tex].

fog(x) = [tex]2\sqrt{(2x - 1}[/tex].

Therefore,  fog(x) = [tex]2\sqrt{(2x - 1}[/tex].