Answers:
[tex](f \circ g)(x) = \sqrt{36x^2+96x+65}\\\\\\(f \circ g)(2) = \sqrt{401}\\\\[/tex]
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Work shown for part 1
[tex]f(x) = \sqrt{x^2-2x+2}\\\\f(g(x)) = \sqrt{(g(x))^2-2(g(x))+2}\\\\f(g(x)) = \sqrt{(-6x-7)^2-2(-6x-7)+2}\\\\f(g(x)) = \sqrt{36x^2+84x+49+12x+14+2}\\\\f(g(x)) = \sqrt{36x^2+96x+65}\\\\(f \circ g)(x) = \sqrt{36x^2+96x+65}\\\\[/tex]
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Work shown for part 2
[tex](f \circ g)(x) = \sqrt{36x^2+96x+65}\\\\(f \circ g)(2) = \sqrt{36(2)^2+96(2)+65}\\\\(f \circ g)(2) = \sqrt{401}\\\\[/tex]
