Find the Domain and Range f(x) = natural log of x-4

Problem

ƒ(x)=ln(x−4)

Solution

1. Identify the domain of the natural logarithm function. The argument of a logarithm must be strictly greater than zero.

2. Set up the inequality for the argument of the function.

x−4>0

3. Solve for x to find the domain.

x>4

4. Determine the range by considering the behavior of the natural logarithm. The function g(u)=ln(u) outputs all real numbers as u varies from 0 to ∞

5. Conclude the range is all real numbers, often written as (−∞,∞)

Final Answer

Domain: *(4,∞), Range: *(−∞,∞)

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