Answer: \(f(f^{-1})(4)=4\).
Step-by-step explanation:
Given, \(f(x)=x^{2} -12\),
which implies
\(f^{-1}(x^{2}-12)=x\).
We have,
\(x^{2}-12=4\\\Rightarrow x^{2}=16\\\Rightarrow x=4,-4.\)
\(\therefore f^{-1}(4)=4,-4.\)
\(f(f^{-1})(4)=f(4)\\\intertext\textup{or}\\f(f^{-1})(4)=f(-4).\)
Also,
\(f(4)=f(-4)=4,\)
\(\therefore f(f^{-1})(4)=4.\)
