Find the Domain x- natural log of x

Problem

ƒ(x)=x−ln(x)

Solution

1. Identify the components of the function ƒ(x)=x−ln(x) The function consists of a linear term x and a logarithmic term ln(x)

2. Determine the domain of the linear term x Since x is a polynomial, it is defined for all real numbers (−∞,∞)

3. Determine the domain of the logarithmic term ln(x) The natural logarithm function ln(u) is defined only when its argument u is strictly greater than zero.

4. Set up the inequality for the argument of the logarithm.

x>0

5. Find the intersection of the domains. The function ƒ(x) is defined only where both x and ln(x) are defined. This occurs when x is in the interval (0,∞)

Final Answer

Domain of *x−ln(x)={[x∈ℝ,x>0]}

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