Answer: The correct option is
(C) [tex]T^{-1}(x,y)\rightarrow \left(\dfrac{1}{5}x,\dfrac{1}{5}y\right).[/tex]
Step-by-step explanation: We are given a transformation T defined as :
[tex]T:(x,y)\rightarrow (5x,5y).[/tex]
We are to find the inverse transformation [tex]T^{-1}(x,y).[/tex]
From the given transformation, we have
[tex]T:(x,y)\rightarrow (5x,5y)\\\\\Rightarrow T^{-1}(5x,5y)=(x,y).[/tex]
Let us consider that
[tex]5x=z~~~~~~\Rightarrow x=\dfrac{z}{5},\\\\\\5y=t~~~~~~\Rightarrow y=\dfrac{t}{5}.[/tex]
Therefore, we get
[tex]T^{-1}(5x,5y)\rightarrow(x,y)\\\\\Rightarrow T^{-1}(z,t)\rightarrow \left(\dfrac{z}{5},\dfrac{t}{5}\right)\\\\\\\Rightarrow T^{-1}(x,y)\rightarrow \left(\dfrac{1}{5}x,\dfrac{1}{5}y\right).[/tex]
Thus, (C) is the correct option.
