Question

Find domain and range of the function f(x) = 1 / 3x-2 ​

Answer 1

Step-by-step explanation:

f(x) = 1 / 3x-2

function f(x) is not defined when 3x-2=0

x=⅔

so, Domain:- R-{⅔}

let f(x)=y

=>y=1/(3x-2)

=>3xy-2y=1

=>3xy=1+2y

=>x=(1+2y)/3y

so,x=(1+2y)/3y is not defined when

3y=0

y=0

so, range:- R-{0}

Answer 2

Given: A function f(x) = 1/(3x - 2)

To find: The domain and range of a function

Solution: We can see function f(x) = 1/(3x - 2) is not defined when (3x - 2) = 0.

x = 2/3 [excluded value]

So, the domain of f(x) = R - {2/3}.

Now let f(x) = y.

Hence,

y = 1/(3x - 2)

⇒ (3x - 2)y = 1

⇒ 3xy - 2y = 1

⇒ 3xy = 1 + 2y

⇒ x = (1 + 2y)3y

As such, x = (1 + 2y)3y is not defined when y = 0.

Therefore, the range of the function f(x) is R - {0}.

Answer: Domain = R - {2/3}

              Range = R - {0}