Time transformation.

Question

In the figure below, I am meant to write $x_2(t)$ in terms of $x_1(t)$. My answer was:

$$x_2 (t)=x_1 \bigg(-\frac{1}{4} t - \frac{1}{4}\bigg)$$

Is this correct?

Answer 1

Let $x_2(t_2)=x_1(at_1+b)$ choose two points to form a system of equations: $$t_2=0\equiv t_1=-1\Rightarrow0=a(-1)+b$$ $$t_2=\frac{1}{4}\equiv t_1=-2\Rightarrow\frac{1}{4}=a(-2)+b$$ Therefore, $$a=b=-\frac{1}{4}$$