Question

Consider the following funtion: f(x) = 2x 3x2 − 3 What is the domain of the function? What is the range of the function?

Answer 1

What is the function

f(x) = 2x / (3x^2 - 3)

???

Domain: R \ {-1 ; 1}

Range: R

Answer 2

Explanation:

Given is a function as

`f(x) = (2x)/(3x^2-3)`

We find that this funciton is undefined for denominator =0

Denominator =0 when

`3x^2-3=0\\x^2=1\\x=1,-1`

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