QQuestionMathematics
QuestionMathematics
What is the domain of the exponential function shown below? f(2$)= 53x
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Answer
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Step 1:I'll solve this problem step by step, carefully following the LaTeX formatting guidelines:
Step 2:: Understand the Function
The given function is $$f(x) = 5^{3x}$$, which is an exponential function with base 5 and exponent $$3x$$.
Step 3:: Determine the Domain of Exponential Functions
For exponential functions of the form $$f(x) = a^{bx}$$, where $$a > 0$$ and $$a \neq 1$$, the domain is always all real numbers.
Step 4:: Verify the Conditions
- The exponent $$3x$$ can take any real number value
- 5 \neq 1
Step 5:: Confirm the Domain
Since all real numbers can be input into this function, the domain is all real numbers.
Final Answer
The domain of f(x) = 5^{3x} is \mathbb{R} (the set of all real numbers), which can be written in interval notation as (-\infty, \infty).
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