Which function has an inverse?

A) ƒ(x) = x2 + 3, x ≤ 1
B) ƒ(x) = x2 + 8x - 9, x ≤ -6
C) ƒ(x) = 2x2 + 8x -4, x ≤ -2
D) ƒ(x) = 2x2 - 4x + 1, x ≥ 3

Question

Which function has an inverse?

A) ƒ(x) = x2 + 3, x ≤ 1	
B) ƒ(x) = x2 + 8x - 9, x ≤ -6	
C) ƒ(x) = 2x2 + 8x -4, x ≤ -2	
D) ƒ(x) = 2x2 - 4x + 1, x ≥ 3

e.mccormick · Answer

All of the equations have some sort of inverse, but the values required might not be valid for it to be a function.  When you take an inverse, it flips the function over the line y=x.  If the result would fail the horizontal line test, it is not a function and therefore the function does not have an inverse even though the equation can be inverted.

e.mccormick · Answer

Horozontall... oops.  I meant vertical line test...

e.mccormick · Answer

Not sure if you are still there. Here is a reference: http://www.purplemath.com/modules/invrsfcn.htm It gets into the restrictions about page 3 and continues with them to the end. Lot of examples for you to look at and get a better idea about this.

e.mccormick · Answer

Another big killer of possible functions is if you would have negative values under a root.  If the resulting function allows for that, well, then it is impossible.