Question

How do you find the domain and range of `f(x) = sqrt x /( x^2 + x - 2)`?

Answer 1

Domain of `x` in interval notation is `[0,1)uu(1,oo)` and range is `RR`.

Explanation:

Here in `f(x)=sqrtx/(x^2+x-2)`

As we have `sqrtx` in numerator, `x` cannot take negative values, hence we should have `x>=0`

Further denominator can be factorized to `(x+2)(x-1)`, hence `x` cannot take values `-2` and `1`,

and hence domain of `x` in interval notation is `[0,1)uu(1,oo)`

However, as `f(x)` can take any value from `-oo` (when `x->1` from left) to `oo` (when `x->1` from right) as degree of denominator is higher than that of denominator. Further, `f(x)=0` when `x=0`..

hence range is `f(x) in RR`

graph{sqrtx/(x^2+x-2) [-7.58, 12.42, -4.96, 5.04]}