Which of the following is/are the polynomial functions? I. f(x)=x3-x2+2 ∀ x ∈ R II. f(x)=x4+√2 x ∀ x ∈ R III. f(x)=x2 / 3+2 x ∀ x ∈ R

Question

Which of the following is/are the polynomial functions? I. f(x)=x3-x2+2 ∀ x ∈ R II. f(x)=x4+√2 x ∀ x ∈ R III. f(x)=x2 / 3+2 x ∀ x ∈ R (A) I, II (B) II, III (C) I, II, III (D) Only I

Tardigrade Admin · Accepted Answer

Polynomial function A function f: R arrow R is said to be polynomial function, if for each x in R, y=f(x)=a0+a1 x+a2 x2+⋅s+an xn, where n is a non-negative integer and a0, a1, a2, ldots, an ∈ R. The function f(x)=x3-x2+2 and f(x)=x4+√2 x are polynomial functions whereas f(x)=x2 / 3+2 x is not a function because in first term power of x is not an integer.

Q. Which of the following is/are the polynomial functions? I. f(x)=x3−x2+2∀x∈R II. f(x)=x4+2​x∀x∈R III. f(x)=x2/3+2x∀x∈R

I, II

II, III

I, II, III

Only I

Q. Which of the following is/are the polynomial functions?
I. $f (x) = x^{3} - x^{2} + 2\forall x \in R$
II. $f (x) = x^{4} + 2 x \forall x \in R$
III. $f (x) = x^{2/3} + 2 x \forall x \in R$