Linear Transformation Help! L(t+1) = t^2 + t - 2 and....

[luckyc1423]

I am really struggling with this topic and have a question that I am having troubling solving can anyone help!?

Let L: P1 --> P2 be a linear transformation for which we know that L(t + 1) = t^2 + t - 2 and L(t - 1) = t^2 - t - 1

find L(6t - 4)

 

[tkhunny]

Have you noticed that 6*t - 4 = (t+1) + 5*(t-1)?

 

[Matt]

Hence:

\(\displaystyle \L\begin{eqnarray}
L(6t-4)
&=&L[(t+1)+5(t-1)]\\
&=&L(t+1)+5L(t-1)
\end{eqnarray}\)