I'm not sure if you mean ( [tex] \sqrt{x + 7} [/tex] ) or ( [tex] \sqrt{x} + 7[/tex] ) I solved it both ways .
[tex]f(x) = \sqrt{x + 7} \\ \\ f( \: g(x) \: ) = \sqrt{(8x - 11)+ 7} \\ = \sqrt{8x - 11 + 7} \\ = \sqrt{8x - 4} \\ = 2 \sqrt{2x - 1} [/tex]
____o_____o______
[tex]f(x) = \sqrt{x} + 7 \\ \\ f( \: g(x) \: ) = \sqrt{(8x - 11)} + 7 \\ = \sqrt{8x - 11} + 7\\ [/tex]
I hope I helped you^_^
