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December 7th, 2010, 11:47 AM   #1
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math analysis

show that f(x) is continuous on R but not differentiable on R

f(x) = (x^2 -1)sin(1/x-1) if x don't equal 1
f(x) = o , if x=1



2/ let f:A?B and C ? B , D ? B prove that ƒ -¹ (C/D) = ƒ -¹ (C)/ƒ -¹(D)
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December 9th, 2010, 05:33 PM   #2
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Re: math analysis

Quote:
Originally Posted by alice 9
show that f(x) is continuous on R but not differentiable on R

f(x) = (x^2 -1)sin(1/x-1) if x don't equal 1
f(x) = o , if x=1



2/ let f:A?B and C ? B , D ? B prove that ƒ -¹ (C/D) = ƒ -¹ (C)/ƒ -¹(D)
How can we know that exercise No 2 is correct ??

IS in exercise No 1 ??
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December 10th, 2010, 10:58 AM   #3
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Re: math analysis

fore q 1 its
(x^2 - 1) sin 1 over (x-1)
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December 11th, 2010, 05:07 PM   #4
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Re: math analysis

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Originally Posted by alice 9
fore q 1 its
(x^2 - 1) sin 1 over (x-1)
To prove that we must prove that left hand side is a subset of the right hand side and conversely.

But for the left hand side to be a subset of the right hand side we must have that:

if ,THEN ).

.........................................OR....... ......(By using the definition of preimage).....................

and ( and ) and .

.................................................. ...OR............................................. .........................

and ( and ) and and

Now can you curry on from here??
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