Given f(x)=√x & g(x)=x^2 . Solve for the following and get the domain and range of the resulting function or relation for g/f.Show complete solution and explain the process and answer.
Dividing the function g by the function f yields:
`(g) /( f) = (x^2)/sqrt x`
Since the new function is a fraction, the x values must not cancel the denominator, hence `sqrt x != 0` .
The denominator requests another restriction such that: x>0.
The domain of the function is the interval `(0;oo).`
The range of the function may be found plugging values from `(0,oo)` in the expression `x^2/sqrt x` .
The range of the function is the same with the domain:`(0,oo).`
Hence, the domain and the range of the function `(g)/(f ) = x^2/sqrt x` are like: `(0,oo).`