Answer
This function is not one-to-one.
Work Step by Step
If the function $f(t)$ represents your height at age $t$ then for each age you would have to have different heights. This is not true because you can, for example, be $1.75$ m tall at certain age, grow a bit more and then shrink back to $1.75$ m. The same value of $f$ would correspond to two different ages $t$ and thus this function won't be one-to-one.
