Answer
No, r(t) is not one-to-one.
Work Step by Step
The function $r(t)=t^4-1$ is not one-to-one because it fails the horizontal line test (even function). We can show that it has the same $y$ value for two different $t$ values:
$f(-1)=(-1)^4-1=1-1=0$
$f(1)=1^4-1=1-1=0$
Thus the function is not one-to-one.
