Emy383idn
Answered

Get the information you need quickly and easily with IDNLearn.com. Discover the information you need from our experienced professionals who provide accurate and reliable answers to all your questions.

Given the functions:
[tex]\[ f(x) = -6x \quad g(x) = |x - 3| \quad h(x) = \frac{1}{x + 5} \][/tex]

Evaluate the function [tex]\(\left(\frac{g}{f}\right)(3)\)[/tex] for the given value of [tex]\(x\)[/tex]. Write your answer.

[tex]\(\left(\frac{g}{f}\right)(3)\)[/tex] is [tex]\(\boxed{\text{undefined}}\)[/tex]

Sagot :

GinnyAnsweridn
To evaluate [tex]\(\left(\frac{g}{f}\right)(3)\)[/tex], we need to do the following steps:

1. Evaluate [tex]\(g(x)\)[/tex] at [tex]\(x = 3\)[/tex].
2. Evaluate [tex]\(f(x)\)[/tex] at [tex]\(x = 3\)[/tex].
3. Calculate [tex]\(\frac{g(3)}{f(3)}\)[/tex] and determine if we have a division by zero.

First, let's evaluate [tex]\(g(x)\)[/tex] at [tex]\(x = 3\)[/tex]:
[tex]\[ g(x) = |x - 3| \][/tex]
[tex]\[ g(3) = |3 - 3| = |0| = 0 \][/tex]

Next, let's evaluate [tex]\(f(x)\)[/tex] at [tex]\(x = 3\)[/tex]:
[tex]\[ f(x) = -6x \][/tex]
[tex]\[ f(3) = -6 \cdot 3 = -18 \][/tex]

Now, let's calculate [tex]\(\frac{g(3)}{f(3)}\)[/tex]:
[tex]\[ \frac{g(3)}{f(3)} = \frac{0}{-18} = 0 \][/tex]

Since we are not dividing by zero in this step, the calculation is valid. So, the value of [tex]\(\left(\frac{g}{f}\right)(3)\)[/tex] is:
[tex]\[ \left(\frac{g}{f}\right)(3) = 0 \][/tex]

Therefore, [tex]\(\left(\frac{g}{f}\right)(3)\)[/tex] is [tex]\(\boxed{0}\)[/tex].
Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. Your search for answers ends at IDNLearn.com. Thanks for visiting, and we look forward to helping you again soon.