Answer:Inverse of y = [tex]f^{-1}(x)[/tex] = [tex]\sqrt{100 -x}[/tex].Step-by-step explanation:Given : f(x) = y = 100 - x²To find : Find inverse.Solution : We have given that : f(x) = y = 100 - x²Step1) : Replace every x with a y and replace every y with an x .x = 100 - y².Step 2): Solve for yOn subtracting 100 from both sidesx - 100 = -y²On multiplying both side by -1100 -x = y²Taking square root both sides and switching sidesy = ± [tex]\sqrt{100-x}[/tex].Step3 ) : Replace y with [tex]f^{-1}(x)[/tex]. [tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{100-x}[/tex].Therefore, inverse of y = [tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{100-x}[/tex].