Question

what is the domain function of x/x2-3x+2

Answer 1

Answer:

domain = R - {1,2}

Step-by-step explanation:

see the following picture!

note that

x^2 - 3x +2 = (x-1)(x-2)

Answer 2

Domain of the function = R - { 1 , 2 }

Given :

The function

$\displaystyle \sf{ \frac{x}{ {x}^{2} - 3x + 2 } }$

To find :

Domain of the function

Solution :

Step 1 of 3 :

Write down the given function

Let f(x) be the given function

Then we have ,

$\displaystyle \sf{ f(x) = \frac{x}{ {x}^{2} - 3x + 2 } }$

Step 2 of 3 :

Find where denominator vanishes

Denominator of the function f(x) = x² - 3x + 2

Now the denominator vanishes

When x² - 3x + 2 = 0

$\displaystyle \sf{ \implies {x}^{2} - (1 + 2)x + 2 = 0 }$

$\displaystyle \sf{ \implies {x}^{2} -x - 2x + 2 = 0 }$

$\displaystyle \sf{ \implies x(x - 1) - 2(x - 1) = 0 }$

$\displaystyle \sf{ \implies (x - 1) (x - 2) = 0 }$

$\displaystyle \sf{ \implies x = 1 \: , \: 2}$

So denominator of the function vanishes at x = 1 , 2

Step 3 of 3 :

Find domain of the function

Since denominator of the function vanishes at x = 1 , 2

Hence domain of the function

= R - { 1 , 2 }

Where R is the set of real numbers

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