Find the domain of the function algebraically:

Question

3 years ago

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Find the domain of the function algebraically:

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Mathematics

1 answer:

BigorU [14] · Answer 1 · 2021-12-02T07:02:39+03:00

The domain of the function is all real numbers except 2 and -1

Step-by-step explanation:

Domain is the set of inputs of a function on which the function is defined.

Given function is:

$R(x) = \frac{x}{x^2-x-2}$

In case of a function involving fraction, the function is undefined if the denominator is zero so in order to find the domain of the function algebraically , we have to find the values on which the function will be undefined

$x^2-x-2 = 0\\x^2-2x+x-2 = 0\\x(x-2)+1(x-2) = 0\\(x+1)(x-2) = 0\\x+1 = 0 => x=-1\\x-2=0 = > x=2$

The function will be undefined on x=-1 and x=2

So,

The domain of the function is all real numbers except 2 and -1

Keywords: Domain, functions

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