Find the domain and range of the following real functions:- (1)f(x)=under root X(square)-3x-4 (2) f(x)=1/X(square)-3x+2 (3) f(x)=x-1/|x-1|

Please ask one question/ query. Please find answers to your first question. For others also,the domain and range can be identified in a similar way. 

 

1. f(x) = root(x²-3x-4)

f(x) = root((x-4)(x+1))

 

Now for f(x) to be real, (x-4)(x+1) >=0

hence, x>=4 or x<=-1. 

 

Domain = (-infinity, -1] union [4, infinity)

For these values of x, f(x) would vary from 0 to infinity

Hence, range = [0, infinity]