Answer: The required value of [tex]f^{'-1}(\pi+7)[/tex] is 2.
Step-by-step explanation: We are given the following value of a function f :
[tex]f(2)=\pi+7.[/tex]
We are to find the value of [tex]f^{-1}(\pi+7).[/tex]
We know that
For any function g(x) = y,
[tex]g^{-1}(y)=x.[/tex]
Applying the above rule in equation (i), we get
[tex]f(2)=\pi+7\\\\\Rightarrow f^{-1}(\pi+7)=2.[/tex]
Thus, the required value of [tex]f^{'-1}(\pi+7)[/tex] is 2.