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Find the range of \[\sqrt{f(x)-g(x)} - \sqrt{f(x)+g(x)}\]

Such that range of \(f(x)\) is \((a,b)\) for all \(x \in R\)

And range of \(g(x)\) is \((c,d)\) \(x \in R\)

Where \[ a,c \in R^{-} \space and \space b,d \in R^{+}\]

\(f(x)\) and \(g(x)\) are continous and both are increasing functions.

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TopNewestDon't you think your question is too vague?? – Ninad Akolekar · 2 years, 2 months ago

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– Kushal Patankar · 2 years, 2 months ago

Yep, i got that now. It was just crazy curiosityLog in to reply

This question is too vague. We cannot proceed further without some information about the functions given . please try to expkain further. – Raghav Vaidyanathan · 2 years, 2 months ago

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– Kushal Patankar · 2 years, 2 months ago

What would be further necessary information.Log in to reply

We may be able to devise a set method or tactics to solve problems like this when f and g are given. We may be able to find a weak range.. Nothing more. – Raghav Vaidyanathan · 2 years, 2 months ago

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– Kushal Patankar · 2 years, 2 months ago

I added some information and hope thats enoughLog in to reply

– Raghav Vaidyanathan · 2 years, 2 months ago

Nope.. Even now, it is ambiguous. Consider something like f(x)=x and g(x)=x+1 for x between some negative number and some positive number. Here, there is no element in range as given expression is undefined everywhere.Log in to reply

Does it matter whether \(f(x)\) and \(g(x)\) are continous? – Kushal Patankar · 2 years, 2 months ago

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