question

"if f(x)=cos^-1(2x-1) and g(x)=x^2/1+x^2 find domain of fog(x)??"

The following should help:

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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).