Question

Which of the following is (are) polynomial function(s)?

• A. $f\left(x\right)=x^3-3$
• B. $f\left(x\right)=a{x}^2+4x-3\forall a\in R$
• C. $f\left(x\right)=\frac{1}{x}-3$
• D. $f\left(x\right)=6$

Answer 1

Answer: (A), (B), (D)

$f\left(x\right)=6$

The polynomial function is of the form $f\left(x\right)=a_n{x}^n+a_{n-1}{x}^{n-1}+a_{n-2}{x}^{n-2}+\cdots +a_0$
where $n\in W$ and $a_n\ne 0$

Clearly, $f\left(x\right)=x^3-3$ is a polynomial function.

$f\left(x\right)=6$ is also a polynomial function of degree $n=0$

$f\left(x\right)=a{x}^2+4x-3$, where $a\in R$
It is also a polynomial function of degree $n=2$ or $n=1$ depending upon $a\ne 0$ or $a=0$.

$f\left(x\right)=\frac{1}{x}-3$
Here, we have exponent of $x$ as $-1$.
$\therefore$ It is not a polynomial function.