Question

please answer this question fast

Answer 1

Answer:

And is down there.....

Step-by-step explanation:

we can write that .....

$f(x) = \frac{1}{1 - {x}^{2} }$

we know that the denominator can't be 0

$1 - {x}^{2} = 0$

or...

$x = + 1 = - 1$

so x can't be +1,-1

so, the domain is R - {+1,-1}

For the range we write f(x) = y then we find x as a function of y.

$y = \frac{1}{1 - {x}^{2} }$

or....

$x = \sqrt{ \frac{y - 1}{y} }$

now it gets complicated......

$\frac{y - 1}{y} \geqslant 0$

1st case:

y - 1 ≥ 0

y ≥ 0

or ,

y ≥ 1

y ≥ 0

it's y € [ 1 , + ∞⟩

2nd case:

y - 1≤ 0

y ≤ 0

or,

y ≤ 1

y ≤ 0

it's y € ⟨- ∞ , 0 ⟩

now we get the union....

y € ⟨- ∞ , 0 ⟩ U [ 1 , + ∞⟩

it's the domain for x as a function of y. Also

the range of the function as x.

so the range is

x € ⟨- ∞ , 0 ⟩ U [ 1 , + ∞⟩

I am done.