The function f(x) = 23x is a linear function where the coefficient of x is 23.
Domain
The domain of a function refers to the set of all possible input values (x-values) that the function can accept. For f(x) = 23x, there are no restrictions on the value of x; you can input any real number. Therefore, the domain is:
Domain: { x | x ∈ ℝ }
Range
The range of a function refers to the set of all possible output values (f(x)-values) that it can produce. Since f(x) = 23x is a linear function with a non-zero slope (23), it can produce every real number as output as x varies over all real numbers.
Thus, the range is also:
Range: { f(x) | f(x) ∈ ℝ }
Conclusion
In summary, the domain and range of the function f(x) = 23x are both the set of all real numbers:
- Domain: { x | x ∈ ℝ }
- Range: { f(x) | f(x) ∈ ℝ }