Question

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

• A. I, II
• B. II, III
• C. I, II, III
• D. Only I

Answer 1

Answer: (A)

Polynomial function A function $f: R \rightarrow R$ is said to be polynomial function, if for each $x$ in $R, y=f(x)=a_0+a_1 x+a_2 x^2+\cdots+a_n x^n$, where $n$ is a non-negative integer and $a_0, a_1, a_2, \ldots, a_n \in R$.
The function $f(x)=x^3-x^2+2$ and $f(x)=x^4+\sqrt{2} x$ are polynomial functions whereas $f(x)=x^{2 / 3}+2 x$ is not a function because in first term power of $x$ is not an integer.