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azamat
3 years ago
15

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

Mathematics
1 answer:
lisabon 2012 [21]3 years ago
6 0

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=\frac{4+\sqrt{4^2-4(5-x)} }{2}

f^{-1}(x)=\sqrt{x-1}+2

or

f^{-1}(x)=-\sqrt{x-1}+2..............Answer

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