Inverses of Quadratic Relations

Inverses of Quadratic Relations

Hey guys! Since Gurnoor takes forever to write the blog post he asked me to do it instead. I'll be talking about Inverses of Quadratic Relations.

There are 4 easy steps to find the Inverse of a Quadratic Relation:

1. Replace f(x) with y.
2. Switch x and y.
3. Solve for y.
4. Replace y with f-1(x)

Example: Algebraically find the inverse of the quadratic whose equation is: 

1) Switch x and y.

x = 2(y - 2)^2 + 3

2)Solve for y.

x-3 = 2(y - 2)^2

(x-3)/2 = (y-2)^2

sqrt[ (x - 3)/2 ] = y-2

The inverse of the quadratic is:{ f(x)= 2 - sqrt[ (x - 3)/2 ]

                                                                  AND

                                                       f-1(x) = 2 + sqrt[ (x - 3)/2 ] }

Graphed it would look like this: 

Horizontal line test

• The horizontal line test is used to determine if a function has an inverse that is also a function. 
• If a horizontal line intersects two or more places the inverse of the function is not a function.

Example: 

• This function fails the horizontal line test so its inverse is not a function

Example 2: 

• This function passes the horizontal line test meaning its inverse is a function.

Hope you guys enjoyed reading.

- SUKH

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 I CHOOSE THIS GUY:

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