Meaning & use
an inverse function
Last updated
Meaning
nouncountablemathematics
A function that undoes the action of another function, mapping each output back to its original input.
Grammar: Countable: use a/an or the, and pluralize with -s.
Patterns
- the inverse function of something
- find the inverse function
- inverse function theorem
The inverse function of f(x) = 2x + 3 is f⁻¹(x) = (x − 3)/2.
Only one-to-one functions have an inverse function.
To solve for x, apply the inverse function to both sides of the equation.
Word forms
| plural | inverse functions |
|---|
Common combinations
- inverse function theorem
- The inverse function theorem gives conditions under which a function has a local inverse.
- find the inverse function
- Students learned to find the inverse function by swapping x and y.
- the inverse function of
- The inverse function of exponentiation is the logarithm.
- inverse function property
- The inverse function property states that f(f⁻¹(x)) = x.
Synonyms and how they differ
- antifunction
- Antifunction is rare and not standard in modern math; inverse function is the correct term.
Word family
Commonly confused: an inverse function or reciprocal?
an inverse function vs reciprocal
Reciprocal means 1 divided by the number (e.g., reciprocal of 2 is 1/2), while inverse function undoes a function's operation.
Practice
If f(x) = x + 5, what is the inverse function f⁻¹(x)?
Choose one answer.
To undo adding 5, you subtract 5, so f⁻¹(x) = x − 5. The other options either repeat the function, multiply, or take the reciprocal, which is not the inverse.
Make it your own
Write a sentence using “an inverse function”, then check it and compare it with the examples above.