Question
Find the domain of the function.
h left parenthesis x right parenthesis equals log Subscript 3 Baseline left parenthesis x minus 3 right parenthesis
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Part 1
The domain of h is
enter your response here.
(Type your answer in interval notation.)
h left parenthesis x right parenthesis equals log Subscript 3 Baseline left parenthesis x minus 3 right parenthesis
Question content area bottom
Part 1
The domain of h is
enter your response here.
(Type your answer in interval notation.)
Answers
GPT-4o mini
To find the domain of the function \( h(x) = \log_3(x - 3) \), we need to determine for which values of \( x \) the logarithm is defined.
The logarithmic function \( \log_b(y) \) is defined only for \( y > 0 \). Thus, for the function \( h(x) \) to be defined, we need:
\[
x - 3 > 0
\]
Solving this inequality gives:
\[
x > 3
\]
Therefore, the domain of \( h \) is all \( x \) such that \( x \) is greater than 3. In interval notation, this is:
\[
(3, \infty)
\]
So, the domain of \( h \) is \( (3, \infty) \).
The logarithmic function \( \log_b(y) \) is defined only for \( y > 0 \). Thus, for the function \( h(x) \) to be defined, we need:
\[
x - 3 > 0
\]
Solving this inequality gives:
\[
x > 3
\]
Therefore, the domain of \( h \) is all \( x \) such that \( x \) is greater than 3. In interval notation, this is:
\[
(3, \infty)
\]
So, the domain of \( h \) is \( (3, \infty) \).