What is the domain of the function `f(x)= 3^(x)` ?

Options

A. `(-oo, oo)`
B. `(0, oo)`
C. `[0, oo)`
D. `(-oo, oo)- {0}`

Answer

To find the domain of the function \( f(x) = 3^x \), we need to determine the set of all possible values of \( x \) for which the function is defined.

### Step-by-Step Solution:

1. **Understanding the Function**: The function \( f(x) = 3^x \) is an exponential function where the base is 3, which is a positive real number.

2. **Identifying the Domain**: The domain of a function consists of all the input values (in this case, \( x \)) for which the function produces a valid output. For exponential functions, they are defined for all real numbers.

3. **Analyzing the Exponent**: Since \( 3 \) is a positive constant, it can be raised to any real number \( x \). This means there are no restrictions on the value of \( x \).

4. **Conclusion**: Therefore, the function \( f(x) = 3^x \) is defined for all real numbers. Hence, the domain of the function is:
\[ \text{Domain} = (-\infty, \infty) \]

### Final Answer:
The domain of the function \( f(x) = 3^x \) is \( (-\infty, \infty) \).

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