mukushla
Range of\[f(x)=\sqrt{x^2+x+2}-\sqrt{x^2+x+1}\]
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hartnn
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\[f(x)=\sqrt{x^2+x+2}-\sqrt{x^2+x+1}\]
mukushla
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yeah
Yahoo!
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Range = Real Numbers
sauravshakya
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I think |dw:1347709678855:dw|
mukushla
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thats it
mukushla
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what is ur approach?
estudier
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always positive, diff for max
sauravshakya
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x^2+x+2=(x+1/2)^2 +7/4
x^2+x+1=(x+1/2)^2+3/4
Now,
f(x) is maximum when (x+1/2)^=0 because the f(x) value decresases as (x+1/2)^2 is greater than 0 since |dw:1347710167952:dw|
Now, when (x+1/2)^2 ---->approaches infinity f(x) will be minimum but will never be zero.....but will be very close to zero
sauravshakya
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Sorry not good at expalining things
sauravshakya
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But I think thats it
mukushla
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\[f(x)=\frac{1}{\sqrt{x^2+x+2}+\sqrt{x^2+x+1}}\]
sauravshakya
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Is that another question?
mukushla
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no this is same
sauravshakya
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?
mukushla
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\[f(x)=\sqrt{x^2+x+2}-\sqrt{x^2+x+1}\times\frac{\sqrt{x^2+x+2}+\sqrt{x^2+x+1}}{\sqrt{x^2+x+2}+\sqrt{x^2+x+1}}\]
hartnn
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just rationalizing the denom, isn't it ?
mukushla
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yes
sauravshakya
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Oh ya