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What is the domain of y=log4(x+3)?
A.all real numbers less than –3
B.all real numbers greater than –3
C.all real numbers less than 3
D.all real numbers greater than 3

Respuesta :

MuchoE
First of all the domain of the logarithm function is all real numbers such that x>0.
When you add 3
all real numbers such that x+3>3 or
the answer
B
all real number such that x>-3.

Answer:

Option B - All real numbers greater than -3.

Step-by-step explanation:

Given : Function [tex]y=\log_4(x+3)[/tex]

To find : What is the domain of function ?

Solution :

The domain is all values of x  that make the expression defined.

Function [tex]y=\log_4(x+3)[/tex]

Applying logarithmic property,

[tex]y=\log_a x\Rightarrow a^y=x[/tex]

[tex]4^y=x+3[/tex]

We know that, exponent is always greater than 0 [tex]x^y> 0[/tex]

So, [tex]4^y>0[/tex]

i.e. [tex]x+3>0[/tex]

[tex]x>-3[/tex]

The domain of the function is [tex]x>-3[/tex]

i.e. All real numbers greater than -3.

Therefore, Option B is correct.