Find the Domain and Range h(x) = natural log of x+5

Problem

h(x)=ln(x+5)

Solution

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

x+5>0

2. Solve the inequality for x to find the domain.

x>−5

3. Express the domain in interval notation.

Domain:(−5,∞)

4. Analyze the behavior of the natural logarithm function to determine the range. The output of ln(u) spans all real numbers as u goes from 0 to ∞

Range:(−∞,∞)

Final Answer

Domain:(−5,∞),Range:(−∞,∞)

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