Reciprocal

Definition

The reciprocal of a number is 1 divided by that number. For a non-zero number $a$, its reciprocal is $\frac{1}{a}$.

5 Must Know Facts For Your Next Test

1. The reciprocal of a fraction $\frac{a}{b}$ is $\frac{b}{a}$.
2. Multiplying a number by its reciprocal results in 1, i.e., $a \cdot \frac{1}{a} = 1$.
3. Zero does not have a reciprocal because division by zero is undefined.
4. In the context of functions, the reciprocal function is $f(x) = \frac{1}{x}$.
5. Reciprocals are used to solve equations involving division and to simplify complex fractions.

Review Questions

• What is the reciprocal of $\frac{3}{4}$?
• Explain why zero does not have a reciprocal.
• If $f(x) = x^2$, what would be the expression for its reciprocal function?

Related terms

Inverse Function: A function that reverses another function such that $f(g(x)) = x$ and $g(f(x)) = x$.

Rational Function: A function represented as the ratio of two polynomials, e.g., $f(x) = \frac{P(x)}{Q(x)}$.

$\text{Multiplicative Inverse}$: $\text{Another term for reciprocal; for any non-zero number } a, \text{ it is } \frac{1}{a}.$