Answered

Find detailed and accurate answers to your questions on IDNLearn.com. Discover the information you need from our experienced professionals who provide accurate and reliable answers to all your questions.

The function [tex]\( F(x) = \log_{0.5} x \)[/tex] is increasing.

A. True
B. False

Sagot :

GinnyAnsweridn
To determine whether the function [tex]\( F(x) = \log_{0.5}(x) \)[/tex] is increasing or not, we need to understand the behavior of logarithmic functions based on the base of the logarithm.

1. Logarithmic Function Basics:
- A logarithmic function [tex]\( \log_b(x) \)[/tex] has a base [tex]\( b \)[/tex].
- The function [tex]\( \log_b(x) \)[/tex] is increasing if [tex]\( b > 1 \)[/tex].
- The function [tex]\( \log_b(x) \)[/tex] is decreasing if [tex]\( 0 < b < 1 \)[/tex].

2. Given Problem:
- Here, the base [tex]\( b \)[/tex] is 0.5.

3. Behavior of Logarithmic Function:
- Since the base of the logarithm in [tex]\( F(x) = \log_{0.5}(x) \)[/tex] is 0.5, which lies between 0 and 1, the function is decreasing.

Thus, the statement "The function [tex]\( F(x) = \log_{0.5}(x) \)[/tex] is increasing" is false.

So, the correct answer is:
B. False
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.