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