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Chapter 1: Problem 1

Find the domain of each function. $$f(x)=3(x-4)$$

Short Answer

Expert verified
The domain of the function \(f(x)=3(x-4)\) is all real numbers.

Step by step solution

01

Identify Type of Function

Since the function \(f(x)=3(x-4)\) is a linear function, recall that linear functions are defined for all real numbers.
02

Detect Restrictions

Linear functions don't have any particular restrictions to their domain. They do not encounter issues with denominators, square roots, or log expressions that could limit the domain. Therefore, the function is defined for all values of x.
03

Conclusion

Since a linear function is always defined for all real numbers, and we have no restrictions on this particular function, we can conclude that the domain for the function \(f(x)=3(x-4)\) is all real numbers.

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