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| Math Central | Quandaries & Queries |
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Question from Juan, a student: The function F is given by F(x)=x^2-6x+13, for x>3. B.Find the inverse function F^-1 C.State the domain of F^-1 |
Juan,
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
and
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,
Penny
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