Mariah D.

asked • 09/10/17

Why does this equation not have an inverse?

f(x)=-4/x2

2 Answers By Expert Tutors

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Kenneth S. answered • 09/10/17

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Let's try to find it.  Interchange variables & solve:
x = 4/y2
 
¼•y2 = 1/x
Now when you solve for the interve, y = ±2 / √x and you see that for any x that is in the domain (non-negatives), you get TWO y values. The graph fails the vertical line test; the inverse is not a function.
 
(Original graph fails HORIZONTAL LINE TEST.)
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Arturo O.

Kenneth,
 
What about the minus sign in the original function?
 
y = -4/x2
 
To invert,
 
x = -4/y2
 
y2 = -4/x
 
y = √(-4/x)
 
 
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09/10/17

Kenneth S.

Well, I have often thought these minus signs in this font are too small.  I totally missed it.
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09/10/17

Arturo O.

It looks like even if we take only the positive square root, we are stuck with a domain restriction where x ≥ 0 is not allowed.  By the way, I spoke to WyzAnt about making the Answer window larger, among other things.  We shall see if they make improvements.
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09/10/17

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