Let $g(x) = x^2 - 11x + 30.$  Find the polynomial $f(x),$ with positive leading coefficient, that satisfies
\[g(f(x)) = x^4 - 14x^3 + 62x^2 - 91x + 42.\]
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<|im_start|>user
Let $g(x) = x^2 - 11x + 30.$  Find the polynomial $f(x),$ with positive leading coefficient, that satisfies
\[g(f(x)) = x^4 - 14x^3 + 62x^2 - 91x + 42.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
x^2 - 7x + 12
Let $g(x) = x^2 - 11x + 30.$  Find the polynomial $f(x),$ with positive leading coefficient, that satisfies
\[g(f(x)) = x^4 - 14x^3 + 62x^2 - 91x + 42.\]
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