1. What is the Negative Reciprocal?

The negative reciprocal of a number is calculated by taking the reciprocal of the number (1 divided by the number) and then changing its sign. Mathematically, the negative reciprocal of x is -1/x.

2. How Does the Calculator Work?

The calculator uses the negative reciprocal formula:

Where:

• \( x \) — Input value (cannot be zero)
• \( f(x) \) — Negative reciprocal of x

Explanation: The calculator simply takes your input value, divides 1 by it, and then negates the result.

3. Applications of Negative Reciprocal

Details: Negative reciprocals are particularly important in mathematics when finding perpendicular lines. The slope of a line perpendicular to another is the negative reciprocal of the original line's slope.

4. Using the Calculator

Tips: Enter any real number except zero. The calculator will return the negative reciprocal of your input. For x=0, the result is undefined (division by zero).

5. Frequently Asked Questions (FAQ)

Q1: Why can't I input zero?
A: The reciprocal of zero is undefined (division by zero is not allowed in mathematics), so the negative reciprocal is also undefined.

Q2: What's the negative reciprocal of 1?
A: The negative reciprocal of 1 is -1 (since 1/1 = 1, then negated is -1).

Q3: What's the negative reciprocal of a negative number?
A: The negative reciprocal of a negative number will be positive. For example, the negative reciprocal of -2 is 0.5.

Q4: How is this used with perpendicular lines?
A: If a line has slope m, any line perpendicular to it will have slope -1/m (the negative reciprocal).

Q5: What's the negative reciprocal of a fraction?
A: For a fraction a/b, its negative reciprocal is -b/a. For example, the negative reciprocal of 3/4 is -4/3.