i. f(x) = x²

Domain of f = R (set of real numbers)

We know that the square of a real number is always positive or equal to zero.

Hence, the range of f is the set of all non-negative real numbers.

Thus, range of f = [0, ∞) = {y: y ≥ 0}

ii. g(x) = sin x

Domain of g = R (set of real numbers)

We know that the value of sine function always lies between –1 and 1.

Hence, the range of g is the set of all real numbers lying in the range –1 to 1.

Thus, range of g = [–1, 1] = {y: –1 ≤ y ≤ 1}

iii. h(x) = x² + 1

Domain of h = R (set of real numbers)

We know that the square of a real number is always positive or equal to zero.

Furthermore, if we add 1 to this squared number, the result will always be greater than or equal to 1.

Hence, the range of h is the set of all real numbers greater than or equal to 1.

Thus, range of h = [1, ∞) = {y: y ≥ 1}