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

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Answer 1 · 2017-08-16T11:46:40

Domain: $x>=0 | x !=1 or [0,1) uu (1,oo)$
Range: $f(x) in RR or (-oo ,oo)$

$f(x) = sqrt(x)/ (x^2+x-2) or f(x) = sqrt(x)/((x-1)(x+2))$

For domain under root should be $>=0 :. x >= 0$ ,

denominator should not be zero , i.e $(x-1) != 0$

$:. x !=1 or (x+2) != 0 or x != -2$ . So restriction is

$x>=0 , x !=1$

Domain: $x>=0 | x !=1 or [0,1) uu (1,oo)$

Range: Any real number , i.e $f(x) in RR or (-oo ,oo)$

graph{sqrt(x)/(x^2+x-2) [-10, 10, -5, 5]} [Ans]

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