$F:\mathbb{R}^3 \rightarrow \mathbb{R}^3, F(x,y,z)=(2x,y,3z+y)$
My current method for these sort of questions is to try to find the matrix that represents this transformation and then see if i can find the inverse of that matrix. Ofcourse, that method takes a long time and im wonderign if there's a better way to do it.
You can find the matrix of this transformation: $$\begin{pmatrix} 2 & 0 & 0\\0 & 1 & 0 \\0&1 &3\end{pmatrix}.$$ Do you see this matrix is inverse?