Respuesta :

pmayl
Remember that you cannot take the log of a negative number, regardless of the base. Also, you can take the logarithm of zero, since no number raised to a power can equal zero (although it come very close). 

Therefore, (x+3), the number inside the logarithm, must be greater than zero. 

x+3 > 0
x > -3 
The domain is x > -3,
or (-3, ∞) in interval notation
MrRoyal

The domain of the function f(x) = log2(x + 3) + 2 is x >= -2.75

How to calculate the domain

The function is given as:

[tex]f(x) = log_2(x + 3) + 2[/tex]

Set to 0

[tex]log_2(x + 3) + 2 = 0[/tex]

Subtract 2 from both sides

[tex]log_2(x + 3) = -2[/tex]

Apply the law of logarithm

[tex]x + 3 = 2^{-2[/tex]

Evaluate the exponent

[tex]x + 3 =0.25[/tex]

Subtract 3 from both sides

[tex]x = -2.75[/tex]

The above means that the smallest value of x is 2.75

Hence, the domain of the function f(x) = log2(x + 3) + 2 is x >= -2.75

Read more about domain at:

https://brainly.com/question/1770447

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