Answer: The required inverse function is [tex]f^{-1}(x)=\dfrac{x-3}{2}.[/tex]
Step-by-step explanation: We are given to find the inverse of the following linear function :
[tex]f(x)=2x+3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Let us consider that
[tex]f(x)=y~~~~~\Rightarrow x=f^{-1}(y).[/tex]
From equation (i), we have
[tex]f(x)=2x+3\\\\\Rightarrow y=2f^{-1}(y)+3\\\\\Rightarrow 2f^{-1}(y)=y-3\\\\\Rightarrow f^{-1}(y)=\dfrac{y-3}{2}\\\\\Rightarrow f^{-1}(x)=\dfrac{x-3}{2}.[/tex]
Thus, the required inverse function is [tex]f^{-1}(x)=\dfrac{x-3}{2}.[/tex]
