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Topic: inverse of a constant function (Read 1674 times) |
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knightfischer
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inverse of a constant function
« on: Apr 8th, 2008, 9:44am » |
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I'm having trouble understanding how to take the inverse of a constant function. I know the technique for f(x)=non-constant function, where you let y=f(x), then interchange x and y and solve for y. But I cannot see how to apply this if there is no x terms.
For example, if:
f(x) = 1, for x>=0
f(x) = -1 for x<0
Then how would you calculate the inverse f^1(x) over the interval (0,3)?
This is from a GRE math prep book I'm studying. Can anyone help?
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towr
wu::riddles Moderator
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Re: inverse of a constant function
« Reply #1 on: Apr 8th, 2008, 9:54am » |
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Well, given
f(x) = 1, for x>=0
f(x) = -1 for x<0
I'd say the best you can say for the inverse is f -1(1) >= 0 and f -1(-1) < 0.
Inverting non-invertible functions isn't really good practice though. There isn't a function f -1(y) such that f -1(f(x)) = x, because f(x) isn't injective (many input-values are mapped to the same output value; so given the output value there is no way to say what the input value was).
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| « Last Edit: Apr 8th, 2008, 9:54am by towr » |
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Wikipedia, Google, Mathworld, Integer sequence DB
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knightfischer
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Re: inverse of a constant function
« Reply #2 on: Apr 9th, 2008, 9:15am » |
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Ok, thanks.
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