I just need someone to check my work before I go on as I am just checking to make sure I am doing it right.
$$g(t) = 2t^2 - 2t ,\ \ \ h(t) = 3t -1$$ $$g(2t^2 - 2t)$$ $$h(g(t)) = 3(2t^2 - 2t) - 1$$ simplified answer of $h(g(t)) = 6t^2 - 6t - 3$
If anything seems off please let me know, Thanks.
$$h(g(t)) = h(2t^2 - 2t) = 3(2t^2 - 2t) - 1 = 6t^2 - 6t - 1$$
You've subtracted $1$ from $g(t)$ and that error follows you when you multiply through by $3$.