How do you find the domain of the following function #g(x) = log_3(x - 4)#?

Answer 1

The domain is #x > 4#.

To find a domain of any logarithmic expression (the base doesn't matter), you need to find out for which #x# the argument of the logarithmic expression is greater than zero.

So, in your case, all you need to do is set

#x - 4 = 0#

and solve this simple equation:

#x = 4#
This means that your domain is #x > 4# and your function is only defined for such #x#.
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Answer 2

To find the domain of the function ( g(x) = \log_3(x - 4) ), we need to consider the values of ( x ) for which the logarithm function is defined. In general, the domain of a logarithm function is all real numbers greater than zero.

However, for the given function ( g(x) = \log_3(x - 4) ), we have an additional constraint. Since the base of the logarithm is ( 3 ), the expression inside the logarithm, ( (x - 4) ), must be greater than zero.

Therefore, we set the inequality ( x - 4 > 0 ) and solve for ( x ):

[ x - 4 > 0 ] [ x > 4 ]

So, the domain of the function ( g(x) = \log_3(x - 4) ) is all real numbers greater than ( 4 ), expressed in interval notation as ( (4, \infty) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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