we are given
[tex]f(x)=x^2-4x+5[/tex]
Since, we have to find inverse of this function
step-1: we set f(x)=y
[tex]y=x^2-4x+5[/tex]
step-2: switch x and y
[tex]x=y^2-4y+5[/tex]
step-3: Solve for y
[tex]y^2-4y+(5-x)=0[/tex]
now, we can use quadratic formula
[tex]y=\frac{4+\sqrt{4^2-4(5-x)} }{2}[/tex]
[tex]f^{-1}(x)=\sqrt{x-1}+2[/tex]
or
[tex]f^{-1}(x)=-\sqrt{x-1}+2[/tex]..............Answer
