Given f(x)=√x and g(x)=x^2 solve for g/f and state the domain and range of the resulting function or relation

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to find the equation of the function `g/f ` such that:

`(g(x))/(f(x)) = (x^2)/sqrt x`

You need to multiply by `sqrt x`  both numerator and denominator to remove the square root from denominator such that:

`(g(x))/(f(x)) = (x^2)*sqrt x/x`

Reducing by x yields:

`(g(x))/(f(x)) = x*sqrt x`

Notice that the equation of function `(g(x))/(f(x)) `  contains the square root function, hence, the radicand needs to be positive such that:

`x gt= 0`

The domain of the function is restricted to interval `[0,oo)` and the range is also the interval `[0,oo)` `` .