Need help in this

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.

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewestDon't you think your question is too vague??

Log in to reply

Yep, i got that now. It was just crazy curiosity

Log in to reply

This question is too vague. We cannot proceed further without some information about the functions given . please try to expkain further.

Log in to reply

What would be further necessary information.

Log in to reply

We do not know anything about the fuctions. First of all we dont know whether they are continuous. Secondly, we dont know what values they take. For example assume f() takes some value in its range for some x, we dont know the respective value of g() for that x.. It may even be possible for the given expression to become undefined. But we cant say anything since we dont know f and g. If f and g are given, then it is possible.. Otherwise, i dont think we can do it.

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.

Log in to reply

Log in to reply

Log in to reply

Does it matter whether \(f(x)\) and \(g(x)\) are continous?

Log in to reply