Inverse means opposite, but it can mean opposite in several ways. In mathematics, inverse variables are a pair in which one increases as the other decreases. Math also offers additive and multiplicative inverses as well as pairs of inverse functions, which take a variable back where it began. In the everyday language of ordinary life, inverse means reversed or opposite, whether in order, direction, nature or effect.
Math: Inverse variables
The farther someone drives, the less gas they have in their tank. If someone drew this situation on a graph, it might appear as a diagonal line, with one quantity decreasing while the other increases. It is an inverse relationship. Other inverse relationships would include altitude and air density, ocean depth and perceived light, gas pressure and volume or vacation days and bank account. One quantity decreases as the other increases.
Math: Additive and multiplicative inverse
The additive inverse of a number is the one added to it to total zero. The additive inverse of the number 1 is -1. The additive inverse of 1,000 is -1,000.
The multiplicative inverse, or reciprocal, of 4 is 1/4, because 4 times 1/4 is 1. The multiplicative inverse of 3/4 is 4/3, or 1 and 1/3. Finding the inverse of some fractions can be painful, but many calculators have a button that does it automatically, marked x-1.
Math: Inverse function
A function is a relationship between one group of numbers and another, such that each number in the first group has exactly one partner in the second group. For example, a function might multiply each number by 2. Then the function of 2 is 4, the function of 3 is 6, the function of 4 is 8 and so on. In math notation, this function is written f(x) = 2x, which means, the function of x is 2 times x.
An inverse function reverses a function, so that the original x reappears. If f(x) = 2x, then f-1(x)=x/2. In other words, the original function multiplies a number by 2, and its inverse function divides the number by 2. Notice that each function is the inverse of the other.
Inverse can mean reversed: The children lined up in alphabetical order facing the cafeteria, and then filed into the gym in inverse order. Or it can mean opposite: He brought her roses from the garden to make her feel better; but she was allergic, so the flowers had the inverse effect.
Occasionally, someone who uses the word inverse is trying for an educated or intellectual effect. Perhaps he or she means to impress listeners with a show of erudition. Unfortunately, people who use a fancy word in a sentence where a straightforward one will communicate more clearly often achieve the inverse.