Common Core Standards: Math
4. Find inverse functions.
A lot of relationships are one way streets. Your students are probably facing that harsh reality in the form of unrequited love. They can buy bouquets of flowers and a heart-shaped boxes of chocolates, but it doesn't mean they'll get any back. Too bad they already ordered that enormous stuffed lovebug.
One-way relationships might be unavoidable in life, but math is much kinder (and your students should remember that). In mathematics, we can have relationships that are two-way streets. They're called inverse functions, and students should know how to find them.
Easier than finding love, anyway.
- Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) = 2x3 or f(x) = (x + 1)⁄(x – 1) for x ≠ 1.
- Verify by composition that one function is the inverse of another.
- Read values of an inverse function from a graph or a table, given that the function has an inverse.
- Produce an invertible function from a non-invertible function by restricting the domain.