Find the Domain cube root of 5x-1 = cube root of 3x-2

Problem

√(3,5*x−1)=√(3,3*x−2)

Solution

1. Identify the type of functions involved in the equation. The equation consists of two cube root functions.

2. Determine the domain of a cube root function. The cube root function ƒ(x)=√(3,g(x)) is defined for all real numbers because the index of the root is odd.

3. Analyze the radicands. The expressions 5*x−1 and 3*x−2 are polynomials, which are defined for all real numbers x

4. Conclude that there are no restrictions on the variable x for the expressions to be defined.

Final Answer

Domain=(−∞,∞)

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