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

1 Answer
Aug 16, 2017

Answer:

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

Explanation:

# 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]