the function $f(x) = \\log_{0.5} x$ is increasing. a. true b. false

$the function $f(x) = \\log_{0.5} x$ is increasing. a. true b. false$

the function $f(x) = \log_{0.5} x$ is increasing.

a. true

b. false

For a logarithmic function $ y = \log_b x $, if $ 0 < b < 1 $, the function is decreasing; if $ b > 1 $, it's increasing.

Here, $ F(x)=\log_{0.5} x $, and $ b = 0.5 $ which satisfies $ 0 < 0.5 < 1 $. So $ F(x) $ is a decreasing function, not increasing.

B. False