Q. 101 - Precalculus Enhanced with Graphing Utilities

Question

Is every odd function one-to-one? Explain.

Step-by-Step Solution

Answer

No, every odd function is not one-to-one because if a function is odd then$f\left(-x\right)=-f\left(x\right)$ and one-to-one implies that $f\left(a\right)=f\left(b\right).$

Step 1. Given Information

We have to explain that is every odd function one-to-one.

Step 2. Explanation

Let the function $f\left(x\right)=\tan x$, it is an odd function but it is not one-to-one. Therefore, every odd function is not one-to-one and we can find out by looking at the following graph, by doing a horizontal line test, we get that the line intersects at many points. Thus, it signifies that the function is not one-to-one.