(i) f(x) = 4x3 -x2 -3x +7 is a polynomial.
(ii) g(x) = 2x3 -3x2 + √x -1 is not a polynomial as exponent of x in √x is not a positive integer.
(iii) p(x) = 2/3 x2 - 7/4x + 9 is a polynomial as all the exponents are positive integers.
(iv) q(x) = 2x2 -3x + 4/x +2 is not a polynomial as exponent of x in 4/x is not a positive integer.
(v) h(x) = x4 - x3/2 +x -1 is not a polynomial as exponent of x in -x3/2 is not a positive integer.
(vi) f(x) = 2+3/x +4x is not a polynomial as exponent of x in 3/x is not a positive integer.