Consider a linear and time$-$invariant $($LTI$)$ system with an impulse response of $h(t)=\{\begin{array}{cc}t+1,& -1t<mn>0</mn>\\ 1-t,& 0t<mn>1</mn>\end{array}.$ For an input signal $x(t),$ the output of the LTI system is $y(t)=\{\begin{array}{cc}t+1,& -1t<mn>0</mn>\\ 1,& 0t<mn>1</mn>\\ 2-t,& 1t<mn>2</mn>\end{array}.$ Such relationship is depicted in Figure Q$1$ below:

Figure Q$1$

a$)$ Show that $x(t)=(t)+(t-1).$

$(5$ marks$)$