Question

Need some help please

Answer 1

Answer:

$x^2\neq -\frac{5}{13}$

First option

Explanation:

Operations with functions

Given two functions f, g, we can perform a number of operations with them including addition, subtraction, product, division, composition, and many others .

We have

$f(x)=20x^3-7x^2+3x-7$

$g(x)=-13x^2-5$

We are required to find

$\displaystyle \frac{f}{g}(x)$

We simply divide f by g as follows

$\displaystyle \frac{f}{g}(x)=\frac{20x^3-7x^2+3x-7}{-13x^2-5}$

We know rational functions may have problems if the denominator can be zero for some values of x. We must find out if there are such values and exclude them from the domain of the new-found function. We must ensure

$-13x^2-5\neq 0$

or equivalently

$x^2\neq -\frac{5}{13}$

Thus the first option is correct

Note: Since $x^2$ is always a positive number (for x real), our function does not really have any restriction in its domain