1. Is the absolute value of 4-x >14 a disjunction or a conjunction?

2. If you have a function what is domain?

1. Is the absolute value of 4-x >14 a disjunction or a conjunction?

Sorry, I do not know those words. Try a Google search.
Now the domain of this is:
4-x > 14 or -(4-x)>14
multiply the left one by -1
*** That means reverse the direction of arrow
x-4 < -14 or x-4 > +14

add 4 to both sides of both
x < -10 or x >18
well the space between x= -10 and x = 18 including the end points is left out of this domain. I suppose that has some meaning in terms of your definitions.

2. If you have a function what is domain?

domain is where the function is defined for the dependent variable.
For example
y = f(x) -1 < x < +1
has a domain between -1 and +1

By the way "range" is the range of y values in that case

Thanks for the help. Does anyone else know if 1 is a disjuncton or conjunction? It's for extra credit before my final.

1. To determine whether the inequality |4 - x| > 14 is a disjunction or a conjunction, let's first analyze its structure.

The absolute value inequality has a greater than symbol, indicating that the expression inside the absolute value must be either strictly greater than the value on the other side of the inequality or strictly less than the negative value of that number. In this case, we have |4 - x| > 14, which means that either 4 - x > 14 or 4 - x < -14.

We can simplify each of these individual inequalities as follows:
- For 4 - x > 14, if we isolate x, we get x < -10.
- For 4 - x < -14, if we isolate x, we get x > 18.

Therefore, the original inequality can be written as a disjunction (using "or" to connect the two inequalities): x < -10 or x > 18.

2. The domain of a function refers to the set of possible input values (also known as the independent variable) for that function. It represents the values for which the function is defined.

To determine the domain of a function, you need to consider any restrictions or limitations on the variable that would make the function undefined. Common restrictions include square roots of negative numbers, divisions by zero, and logarithms of non-positive numbers.

For example, the domain of a function involving a square root would exclude any negative numbers within the square root since it is not defined for negative values.

To find the domain of a specific function, you'll need to analyze the function itself and identify any such restrictions based on the type of operations used (e.g., square roots, divisions, logarithms, etc.) and the values that the variable can take.

In some cases, the domain of a function can be the entire set of real numbers, denoted as (-∞, +∞), meaning there are no restrictions on the input values.