Answer: The inverse of the given function is [tex]y=2x-6.[/tex]
Step-by-step explanation: We are given to find the inverse of the following linear function :
[tex]y=\dfrac{1}{2}x+3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`(i)[/tex]
The inverse of y = f(x) is written as
[tex]x=f^{-1}(y).[/tex]
Substituting the above in equation (i), we get
[tex]y=\dfrac{1}{2}x+3\\\\\Rightarrow y=\dfrac{1}{2}f^{-1}(y)+3\\\\\Rightarrow \dfrac{1}{2}f^{-1}(y)=y-3\\\\\Rightarrow f^{-1}(y)=2(y-3)\\\\\Rightarrow f^{-1}(y)=2y-6.[/tex]
Thus, the inverse of the given function is [tex]y=2x-6.[/tex]
