Question

find the domain and range

Answer 1

Is there any x which makes the function invalid? Are there y's which you can't get? Those are the questions that question is really asking.

Answer 2

well i got
domain = all real nos except -1, 1
and now wanna find range

Answer 3

Domain is good! Let's see what the rest of the values do to y...

Answer 4

Clearly the denominator cannot be greater than one, because \[\frac{1}{1-x^{2}} \]
the \[x^{2}\] will always be greater than or equal to zero.

Answer 5

So the denominator drops towards zero, what happens to the y values?

Answer 6

hmm
i solve it like this
let y = f(x)
y= 1/(1-x^2)
from here,
x= underroot (y-1)/underoot y
now how to move ahead , i dont know

Answer 7

I find it easier to visualize the graph. As 1-x^2 gets closer to zero, the values of y shoot towards infinity. The same happens on the negative side, so now the only question is whether there are certain positive or negative values which are smaller.

Answer 8

Here's something you could try: can y=1/2?

Answer 9

but how

Answer 10

That's the question. If y=1/2, 1-x^2=2, and x^2=-1. That's a problem. In fact, any y between 0 and 1 has that issue.

Answer 11

i didn't understand this point

Answer 12

y cannot be between 0 and 1. y=0 would require x=infinity, and y=1-.000000001 would require 1-x^2 to be >1, which means x^2 would be negative. Any other area works for the range. The graph looks roughly like this: ( in next post )

Answer 13

the easier way to find the range it from the graph
anallitically is very dificult