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For each of the following functions, determine if it is a polynomial, rational function, both, or neither. (a) \( f(x)=\left(-4 x^{7}-3\right)^{6} \) Polynomial function only Rational function only Both polynomial and rational function Neither polynomial nor rational function (b) \( g(x)=\frac{4 x^{7}-x^{2}}{2 x^{7}+\sqrt{x}-6} \) Polynomial function only Rational function only Both polynomial and rational function Neither polynomial nor rational function (c) \( h(x)=-9 x^{-7}-5 x^{-4}+3 \) Polynomial function only Rational function only Both polynomial and rational function Neither polynomial nor rational function (d) \( j(x)=\left(-7 x^{2}+2 \sqrt{x}+1\right)^{2} \) Polynomial function only Rational function only Both polynomial and rational function Neither polynomial nor rational function