Answer: The required values are
[tex]f^{-1}(x)=x-4~~~~~~~~\textup{and}~~~~~~~~~f^{-1}(4)=0.[/tex]
Step-by-step explanation: We are given the following function f(x) :
[tex]f(x)=x+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We are to find the values of [tex]f^{-1}(x)[/tex] and [tex]f^{-1}(4).[/tex]
Let us consider that
[tex]y=f(x)~~~~~~~~\Rightarrow x=f^{-1}(y).[/tex]
So, from equation (i), we get
[tex]f(x)=x+4\\\\\Rightarrow y=f^{-1}(y)+4\\\\\Rightarrow f^{-1}(y)=y-4\\\\\Rightarrow f^{-1}(x)=x-4.[/tex]
Substituting x = 4 in the above equation, we get
[tex]f^{-1}(4)=4-4=0\\\\\Rightarrow f^{-1}(4)=0.[/tex]
Thus, the required values are
[tex]f^{-1}(x)=x-4~~~~~~~~\textup{and}~~~~~~~~~f^{-1}(4)=0.[/tex]
