Question

The function f(x)=log0.5 x is decreasing true or false?

Answer 1

decreasing, so its True

Explanation:

Answer 2

True

Explanation:

Given is a function of logrithm to base 0.5

`f(x) = log_(0.5) x`

This we can write as

`f(x)= log x/log 0.5`

by changing the base to e.

f(x) will be decreasing if f'(x)<0

Let us find f'(x)

`f'(x) = (1)/(x log 0.5)`

is the derivative

We know log x is defined only for positive values of x.

Hence x>0

log 0.5 is always less than 0 since 0.5<1

So f'(x) <0 for all x in the domain

This implies f(x) is decreasing

True