How do you find the domain of #f(x)=|3x-2|#?

Answer 1

The domain is all real numbers, or #RR#.

The domain of a function, is the set containing all possible values the independent variable is "allowed" to take, in order for the function to be well-defined. There is no possible way #abs(3x - 2)# can be undefined for a real #x#, so there are no restrictions on the domain of this real function.

Therefore, the domain is all real numbers.

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Answer 2

Xavier Alonso

To find the domain of the function (f(x) = |3x - 2|), we need to determine for which values of (x) the function is defined.

The absolute value function (|3x - 2|) is defined for all real numbers (x), because the expression inside the absolute value bars can take any real value.

Therefore, the domain of (f(x) = |3x - 2|) is all real numbers, or ((-∞, ∞)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.