Question

What is the inverse of x^2-4x+5

Answer 1

we are given

`f(x)=x^2-4x+5`

Since, we have to find inverse of this function

step-1: we set f(x)=y

`y=x^2-4x+5`

step-2: switch x and y

`x=y^2-4y+5`

step-3: Solve for y

`y^2-4y+(5-x)=0`

now, we can use quadratic formula

`y=(4+√(4^2-4(5-x)) )/(2)`

`f^(-1)(x)=√(x-1)+2`

or

`f^(-1)(x)=-√(x-1)+2`..............Answer