Find the domain and range of a function f(x)=1/(1-x^2)

F(x)=1/(1-x^2)=1/((1-x)(1+x))
F( x) is undefined for x=1 & x=-1
F(x) =1 @ x=0
Rap

F(x)=1/(1-x^2)=1/((1-x)(1+x))
F( x) is undefined for x=1 & x=-1
F(x) =1 @ x=0
Rap

since function defined all real number except x=+1,-1
and range will be closed interval 1 to open interval infinity

I am struggling with these in particular, if someone would be so kind to show how the answer is found that would be great, thanks!
Demonstrate that integrate (cos^m(x) cos^n(x)) with upper limit is (pi/2), lower limit is 0 dx; = ((m/(m+n)) integrate (cos^m-1(x) cos(n-1)x with upper limit is (pi/2), lower limit is 0 dx. Hence, deduce that integrate (cos^m(x) cos(nx) dx = (pi/(2^(n+1)) with upper limit is (pi/2), lower limit is 0 .