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.

1 Answer

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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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).`