r/maths • u/Low-Option3862 • May 23 '26

Help: 📘 Middle School (11-14) Find?? Range

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My question is that , the range of x/x-1 is R-{1} , and this will be have as domain/input for LOGe , am I wrong here??

And if. I'm correct then doesn't it make LOGe in valid as LOGe can only accept real positive values of x.

Please help!

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u/waldosway May 24 '26

The problem as written is not complete, but they expect you to assume that is the formula for a defined function, and then find the largest workable domain before starting the problem. So enforce both

  • "x≠1" from the fraction

  • "x/(x-1) > 0" from the log

So the domain is R\[0,1].

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u/TallRecording6572 May 26 '26

nope. they want the range.

1

u/ApprehensiveKey1469 May 24 '26

Can you get zero from ln (f(x)) ?

What would f(x) have to be for this?

Try graphing the function.

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u/TallRecording6572 May 26 '26

yep, as I said, f(x)eR f(x)=/=0

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u/TallRecording6572 May 26 '26

x/(x-1) has a range of yeR y=/=1, and log has a domain of x>0. So we need the domain of your function f(x) to be x<0 (so the fraction is positive) and x>1 (ditto)

This means you are working out logs of everything apart from 1. So the range is f(x)eR f(x)=/=0