Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
To determine the value of [tex]\( f(-1/7) \)[/tex] for the function [tex]\( f(x) = \frac{4x - 3}{1 + 7x} \)[/tex], we need to follow these steps.
1. Substitute [tex]\( x \)[/tex] with [tex]\(-\frac{1}{7}\)[/tex] in the function [tex]\( f(x) \)[/tex].
[tex]\[ f\left(-\frac{1}{7}\right) = \frac{4\left(-\frac{1}{7}\right) - 3}{1 + 7\left(-\frac{1}{7}\right)} \][/tex]
2. Simplify the numerator:
[tex]\[ 4\left(-\frac{1}{7}\right) - 3 = -\frac{4}{7} - 3 \][/tex]
Convert -3 into a fraction with a common denominator:
[tex]\[ -\frac{4}{7} - 3 = -\frac{4}{7} - \frac{21}{7} = -\frac{25}{7} \][/tex]
3. Simplify the denominator:
[tex]\[ 1 + 7\left(-\frac{1}{7}\right) = 1 - 1 = 0 \][/tex]
4. Compute the value of the function:
[tex]\[ f\left(-\frac{1}{7}\right) = \frac{-\frac{25}{7}}{0} \][/tex]
Since the denominator is zero, the value is undefined, which means it approaches infinity.
Therefore, the correct answer is:
[tex]\[ \boxed{\infty} \][/tex]
1. Substitute [tex]\( x \)[/tex] with [tex]\(-\frac{1}{7}\)[/tex] in the function [tex]\( f(x) \)[/tex].
[tex]\[ f\left(-\frac{1}{7}\right) = \frac{4\left(-\frac{1}{7}\right) - 3}{1 + 7\left(-\frac{1}{7}\right)} \][/tex]
2. Simplify the numerator:
[tex]\[ 4\left(-\frac{1}{7}\right) - 3 = -\frac{4}{7} - 3 \][/tex]
Convert -3 into a fraction with a common denominator:
[tex]\[ -\frac{4}{7} - 3 = -\frac{4}{7} - \frac{21}{7} = -\frac{25}{7} \][/tex]
3. Simplify the denominator:
[tex]\[ 1 + 7\left(-\frac{1}{7}\right) = 1 - 1 = 0 \][/tex]
4. Compute the value of the function:
[tex]\[ f\left(-\frac{1}{7}\right) = \frac{-\frac{25}{7}}{0} \][/tex]
Since the denominator is zero, the value is undefined, which means it approaches infinity.
Therefore, the correct answer is:
[tex]\[ \boxed{\infty} \][/tex]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.