"Determine which functions are polynomial functions. For those..." was answered by our community

vetrila10

Answered question

2021-11-17

Determine which functions are polynomial functions. For those that are, identify the degree.

f (x) = \frac{(x^{2} + 7)}{x^{3}}

Answer & Explanation

Novembruuo

Beginner2021-11-18Added 26 answers

Step 1
Given:

f (x) = \frac{(x^{2} + 7)}{x^{3}}

To Determine:
Whether the given function is polynomial or not.
If polynomial then find the degree of the polynomial.
Step 2
Concept:
A polynomial is a function of the form

f (x) = a_{0} + a_{1} x + a_{2} x^{2} + \dots \dots . + a_{n} x^{n}

Degree of the polynomial is the heighest power of variable (here x).
In polynomial all the exponent (i.e. power of x) must be non-negative integer.
Explanation:

f (x) = \frac{(x^{2} + 7)}{x^{3}} = \frac{x^{2}}{x^{3}} + \frac{7}{x^{3}} = x^{2 - 3} + 7 x^{- 3} = x^{- 1} + 7 x^{- 3}

\Rightarrow f (x) = x^{- 1} + 7 x^{- 3}

Here, we get the power of x in f(x) are negative integers.

\Rightarrow f (x)

is not a polynomial.
Step 3
Answer:

f (x) = \frac{x^{2} + 7}{x^{3}}

is not a polynomial.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Differential Calculus

Didn't find what you were looking for?