Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.5 The First Shifting Theorem - Problems - Page 694: 12

$f(t)=t^2$

We are given that $x=t-1$ Re-write as: $t=x+1$ When $a$ has a positive value then , shift the function to the right for $a$ units and when $a$ has a negative value then , shift the function to the left for $a$ units Now, $f(t-1) =(t-1)^2$ and $f(x)=(x+1-1^2 =x^2$ So, we have: $f(t)=t^2$