Math CentralQuandaries & Queries


Question from Juan, a student:

The function F is given by F(x)=x^2-6x+13, for x>3.
A. Write F(x) in the form (x-a)^2+b

B.Find the inverse function F^-1

C.State the domain of F^-1


Look at my note to another student on completing the square and use it to write y = x2 - 6x + 13 in the form y = (x-a)2 + b. Solve this equation for x by writing (x-a)2 = y - b and taking the square root of both sides. This gives two solutions

x = √(y - b) + a


x = -√(y - b) + a

To decide which is the inverse of F(x) draw a sketch of y = x2 - 6x + 13. You may find it helpful to use the form y = (x-a)2 + b when constructing the graph.

I hope this helps,

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