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

1 Answer
Shwetank Mauria
Apr 30, 2017

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]}

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