Mathematics: Find domain of the function (f/g)(x), given f(x)=x^2-3x-18 and g(x)=x^2-36

Step-by-step explanation:Given that, a regular octagon is to be constructed.To find:Each angle in the octagon = ?Solution:We know that a regular triangle (polygon with 3 sides) has an interior angle of .And a regular quadrilateral (square) has an interior angle of .Therefore, formula for interior angle of a regular polygon with number of sides can be given as:For an octagon, we have .Value of Interior angle in a regular octagon:Kindly refer to the attached image for the angle of...

Find domain of the function (f/g)(x), given f(x)=x^2-3x-18

Ответ:

shermoisllo3

13.01.2022

Mathematics

$\displaystyle \mathbb{R}-\left \{ -6,\ 6 \right \}$

Step-by-step explanation:

Domain of Functions

Given a function h(x), we call the domain of h, all the values x can take so h exists. It's commonly easier to find the values of x for which h does NOT exist and then exclude them from the general domain of the real numbers.

The question provides us with the following functions

$\displaystyle f(x)=x^2-3x-18$

$\displaystyle g(x)=x^2-36$

$\displaystyle h(x)=\frac{x^2-3x-18}{x^2-36}$

We called h(x) to the newly created function f/g(x)

To investigate the possible points of nonexistence for h, we factor h(x)

$\displaystyle h(x)=\frac{(x-6)(x+3)}{(x-6)(x+6)}$

We can clearly see the denominator has two zeros at

$\displaystyle x=6,\ x=-6$

A rational function cannot exist where the denominator is zero, regardless of the possible simplification with the numerator, as in this case. For example, for x=6 the function gets the value 0/0 and it's not defined there. We cannot simplify the common factor because they are part of the original function.

So, the domain of h is

$\displaystyle (-\infty,\ -6 )\bigcup (-6,\ 6)\bigcup (6,+\infty )$