Question

The domain of the function

f(x) = loge(3x – 33x) is


[0, ∞)


(–∞, 0]


(–∞, 0)


(0, ∞)

Answer 1

Answer:

x ∈ ( - ∞ , 0 )

Step-by-step explanation:

Given :

$\displaystyle \sf f(x)=\log_e(3x-33x)$

We have to find domain of f ( x ).

We all know that log function always take positive value i.e. :

If ㏒ₓ a = α then :

= >  a > 0

= > Range y ∈ ( - ∞ , ∞ )

For given question :

= > 3 x - 33 x > 0

= > - 30 x > 0

Multiply by minus sign we get :

= > 30 x < 0

Dividing by 30 we get :

= > x < 0

In interval form , x ∈ ( - ∞ , 0 )

Hence we get required answer!