Find the domain function!
15) f(x) = ln ((x÷3)2)
A)(-∞,3)u(3,∞)
B)(-3,∞)
C)(-∞,-3)u(-3,∞)
D)(-∞,∞)
Please explain!

Question

Find the domain function!
​15) f(x) = ln ((x÷3)2) ​​ 
A)(-∞,3)u(3,∞)​ 
B)(-3,∞)​ 
C)(-∞,-3)u(-3,∞)​ 
D)(-∞,∞) 
Please explain!

helder_edwin · Answer

can u find the logarithm of zero or a negative number?

anonymous · Answer

Idk but I just noticed I made a mistake on the equation. It's supposed to be f(x) = ln ((x÷3)^2)

helder_edwin · Answer

ok.

well u cannot.

so whatever is inside a logarith HAS to be positive. therefore u have to solve the inequality
$$\large (x/3)^2>0 $$

ranga · Answer

Are you sure the question is not f(x) = ln ((x-3)^2) ​​ (x minus 3 rather than x divided by 3)?

helder_edwin · Answer

yes

helder_edwin · Answer

using what u wrote
$$\large (x\div 3)^2>0 $$

(it is the same)

helder_edwin · Answer

now notice u have a squared number on the left.

ranga · Answer

With (x ÷ 3)^2 > 0 (with x divided by 3),
x cannot be 0.  All other x is allowed.  None of the answer choices fit.

With (x - 3)^2 > 0 (with x minus 3),
x cannot be 3.  All other x is allowed.  The first answer choice fits