If #f(x) = x^2  x# and #g(x) = 3x + 1# how do you find #g(f(sqrt2))#?
To find ( g(f(\sqrt{2})) ), first, find ( f(\sqrt{2}) ) by substituting ( \sqrt{2} ) into the function ( f(x) = x^2  x ). Then, take the result and substitute it into the function ( g(x) = 3x + 1 ) to find the final answer.

Find ( f(\sqrt{2}) ): [ f(\sqrt{2}) = (\sqrt{2})^2  \sqrt{2} = 2  \sqrt{2} ]

Substitute ( f(\sqrt{2}) = 2  \sqrt{2} ) into ( g(x) = 3x + 1 ): [ g(2  \sqrt{2}) = 3(2  \sqrt{2}) + 1 = 6  3\sqrt{2} + 1 = 7  3\sqrt{2} ]
So, ( g(f(\sqrt{2})) = 7  3\sqrt{2} ).
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