If `f(x)=sqrt(x-1)/(x-4)` defines a function of R, then what is its domain?

If f(x) = x^2 + 4 is a function defined on f : R rarr [ 4, oo ) , then its inverse function, defined as f^-1 (x) , is:

f(x)=1/sqrt(x^(12)-x^(9)+x^(4)-x+1) . Then domain of function f(x) is

The domain and range of the real function f defined by f(x)=(4-x)/(x-4) is (a) Domain =R , Range ={-1,2} (b) Domain =R -{1}, Range R (c) Domain =R -{4}, Range ={-1} (d) Domain =R -{-4}, Range ={-1,1}

The function f:A rarr R,f(x)=(1)/(sqrt(4x^(2)-1))+ln(x(x^(2)-1)) , f:A rarr R,f(x)=(1)/(sqrt(4x^(2)-1))+ln(x(x^(2)-1)) is (Here A is the largest possible domain of the given function

If f is a real function defined by f(x)=(log(2x+1))/(sqrt3-x) , then the domain of the function is

Statement 1 : The domain of the function f(x)=sqrt(x-[x])" is "R^(+) Statement 2 : The domain of the function sqrt(f(x)) is {x : f (x) ge 0} .

Statement 1 : The domain of the function f(x)=sqrt(x-[x])" is "R^(+) Statement 2 : The domain of the function sqrt(f(x)) is {x : f (x) ge 0} .