Find the Domain and Range y = log of x-2+1

Problem

y=(log_)(x−2)+1

Solution

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

x−2>0

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

x>2

3. Determine the range of the function. Since the parent function y=(log_)(x) has a range of all real numbers, and the transformations (horizontal shift, vertical shift) do not restrict the output values, the range remains all real numbers.

−∞<y<∞

Final Answer

Domain: *(2,∞), Range: *(−∞,∞)

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