how do i find the domain?

Question

in this problem

F(x)=3x+2/ x^2-4x+4

Answer 1

Since division by zero is undefined, the domain excludes those values.
Set the denominator equal to zero & solve:
x^2 - 4x + 4 = 0
(x - 2)(x - 2) = 0
x = 2.
The domain is all Real numbers, except 2.

Answer 2

if u first factorize the denominator u will get (x-2)^2.
now, f(x)=3x+2/(x-2)^2

domain is the set of those values for which f(x) is always real.we can't inculde those values of x in the domain for which f(x) becomes imaginary or infinity.
here, if we set x=2 then the denominator becomes 0 and thus f(x) becomes infinity. so the domain of f(x) will be all real numbers except 2.
domain f = R- {2}; where R is the set of real numbers.

Answer 3

whatever the value of x that makes the expression on the denominator equals to 0 is the restriction or domian.

x^2 - 4x + 4 = 0
(x - 2)^2 = 0
x = 2

so, x can be any real numbers, except 2

Answer 4

The denominator can be factored as (x-2)^2.

The domain is all real numbers excluding 2.

Answer 5

The domain just means what values of X are allowed.

In this case, you can use any x except x=0. So the domain is - infinity to + infinity, excluding zero.