"if f(x)=cos^-1(2x-1) and g(x)=x^2/1+x^2 find domain of fog(x)??"
The following should help:
The domain refers to all allowable values of x. Here that is from -infinity to + infinity (R)
The range refers to the resulting values of y (or fog(x)). Since (x^2 -1)/(x^2 + 1) can range from -1 (when x is 0) to +1 (when the absolute value of x is very large) then the angle whose cosine is (x^2 -1)/(x^2 + 1) can be any positive or negative value. So the range is -infinity to +infinity as well (R).