Find the Domain and Range f(x) = log of x-7

Problem

ƒ(x)=(log_)(x−7)

Solution

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

2. Set up the inequality for the argument.

x−7>0

3. Solve the inequality for x

x>7

4. Express the domain in interval notation.

Domain: *(7,∞)

5. Determine the range of the logarithmic function. Since the base is not specified, it is assumed to be 10 or e A basic logarithmic function ƒ(x)=(log_)(u) can output any real number as u varies from 0 to ∞

6. Express the range in interval notation.

Range: *(−∞,∞)

Final Answer

ƒ(x)=(log_)(x−7)⇒Domain: *(7,∞), Range: *(−∞,∞)

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