Suppose the domain of f is (-1,1). Define the function l by l(x)= f(x+1/x-1). What is the domain of l?

waffles
Oct 25, 2017

#1**+1 **

The domain of f(x) is -1 < x < 1

So the domain of f( \(\frac{x+1}{x-1}\) ) is -1 < \(\frac{x+1}{x-1}\) < 1

*edit* (I was unhappy with my previous answer.)

The easiest way to find the x values that make this inequality true is to look at a graph.

So the x values that make -1 < \(\frac{x+1}{x-1}\) < 1 true are x < 0 .

The domain of f( \(\frac{x+1}{x-1}\) ) is (-∞ , 0)

The domain of l(x) is (-∞ , 0) .

hectictar
Oct 25, 2017

#2**+1 **

One question, hectictar...

You write that

" So the x values that make -1 < (x +1) / (x - 1) < 1 true will either be x < 0 or x > 0 ."

How did you determine this ???

CPhill
Oct 25, 2017

#3**+1 **

x + 5 < 8

If for some reason we cant solve this inequality the normal way, then we can do it like this

x + 5 = 8

x = 3

And then we know that

the values that make the original inequality, x + 5 < 8 , true will be either x < 3 or x > 3 .

I thought about it because when you are trying to find the values that make a quadratic function greater or less than zero, we have to do it like this and test points in an interval.

....Is that a good explanation??

hectictar
Oct 25, 2017