Answer:
What is the function
f(x) = 2x / (3x^2 - 3)
???
Domain: R \ {-1 ; 1}
Range: R
Answer:
Step-by-step explanation:
Given is a function as
[tex]f(x) = \frac{2x}{3x^2-3}[/tex]
We find that this funciton is undefined for denominator =0
Denominator =0 when
[tex]3x^2-3=0\\x^2=1\\x=1,-1[/tex]
Hence function is not defined for x=1,-1
Domain is R-{-1,1}
To find range:
We see that denominator has degree 2 and numerator degree 1
i.e. denominator has more degree of x then numerator
Hence y=0 is horizontal asymptote
But when y=0 we have x=0
Hence though there is a horizontal asymptote range is the set of all real numbers
Domain = R-{-1,1}
Range = R
