+647 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?
+9479 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) .
+129852 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 ???
+9479 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??
