### Home > CALC > Chapter 2 > Lesson 2.1.2 > Problem 2-27

2-27.

If the inverse of *f*(*x*) is a continuous function, why must *f*(*x*) be either strictly increasing or decreasing? Sketch an example to support your reasoning. Homework Help ✎

Strictly increasing means, as *x* increases, *y*-values are always going up.

Strictly decreasing means, as *x* increases, *y*-values are always going down.

If a function is NOT strictly increasing or decreasing, then either

I. it oscillates between increasing and decreasing

II. it is horizontal always or sometimes

As you sketch, try to find a counter-example to this statement. In other words, try to sketch a function with a continuous inverse function that is NOT strictly increasing or strictly decreasing.

Note that *f*(*x*) and its inverse must both be continuous AND both be functions.