Question

Find the domain of the function and express the domain in interval notation. $$h(x)=\log (6-2 x)$$

Name: Problem 88, Chapter 8: Intermediate Algebra
Uploaded: 2020-06-23T08:51:37-08:00
Duration: 38 s
Channel: Ankit Gupta
Description: Find the domain of the function and express the domain in interval notation. h(x)=log(6-2 x)

   Find the domain of the function and express the domain in interval notation.
$$h(x)=\log (6-2 x)$$

Intermediate Algebra

Julie Miller, Molly… 5th Edition

Chapter 8, Problem 88

Instant Answer

Solved by Expert Ankit Gupta

06/23/2020

Step 1

This is because the logarithm function is only defined for positive numbers. So, we have the inequality: $$6-2x > 0$$ Show more…

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Find the domain of the function and express the domain in interval notation. $$h(x)=\log (6-2 x)$$

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Key Concepts

Domain

The domain of a function is the complete set of all possible input values (x-values) that the function can accept without causing any undefined behavior, such as division by zero or taking the logarithm of a non-positive number.

Logarithmic Functions

Logarithmic functions, by definition, require their arguments to be positive. In other words, for a logarithm log(a) to be defined in the real numbers, the argument a must be greater than zero.

Inequality Solving

To determine the domain of a function involving a logarithm, one sets up an inequality by requiring that the argument of the logarithm be strictly greater than zero, and then solves that inequality for the variable.

Interval Notation

Interval notation is a method of writing subsets of the real numbers. It uses parentheses or brackets to show whether endpoints are excluded or included, providing a concise way to represent continuous ranges of valid input values.

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