Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To find the domain of the function [tex]\( y = \log(1 - 2x) \)[/tex], we need to determine the values of [tex]\( x \)[/tex] for which the argument of the logarithm is positive, as the logarithmic function is only defined for positive arguments.
1. Start by identifying the condition for the argument of the logarithm to be positive:
[tex]\[ 1 - 2x > 0 \][/tex]
2. Solve the inequality:
[tex]\[ 1 - 2x > 0 \][/tex]
Subtract 1 from both sides:
[tex]\[ -2x > -1 \][/tex]
Divide both sides by -2. Remember that dividing by a negative number reverses the inequality:
[tex]\[ x < \frac{1}{2} \][/tex]
3. This inequality tells us that [tex]\( x \)[/tex] must be less than [tex]\( \frac{1}{2} \)[/tex].
So, the domain of the function [tex]\( y = \log(1 - 2x) \)[/tex] in interval notation is:
[tex]\[ (-\infty, \frac{1}{2}) \][/tex]
Thus, the domain is:
[tex]\[ \boxed{(-\infty, \frac{1}{2})} \][/tex]
1. Start by identifying the condition for the argument of the logarithm to be positive:
[tex]\[ 1 - 2x > 0 \][/tex]
2. Solve the inequality:
[tex]\[ 1 - 2x > 0 \][/tex]
Subtract 1 from both sides:
[tex]\[ -2x > -1 \][/tex]
Divide both sides by -2. Remember that dividing by a negative number reverses the inequality:
[tex]\[ x < \frac{1}{2} \][/tex]
3. This inequality tells us that [tex]\( x \)[/tex] must be less than [tex]\( \frac{1}{2} \)[/tex].
So, the domain of the function [tex]\( y = \log(1 - 2x) \)[/tex] in interval notation is:
[tex]\[ (-\infty, \frac{1}{2}) \][/tex]
Thus, the domain is:
[tex]\[ \boxed{(-\infty, \frac{1}{2})} \][/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.