To find ( f(g(2)) ), first calculate ( g(2) ). Given ( g(x) = x^2 - 6x + 7 ), substituting ( x = 2 ) gives ( g(2) = 2^2 - 6 \cdot 2 + 7 = 4 - 12 + 7 = -1 ). Next, use this result in ( f(x) = x + 8 ) to find ( f(-1) = -1 + 8 = 7 ). Therefore, ( f(g(2)) = 7 ).
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