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:
[tex]R(x) = \frac{x}{x^2-x-2}[/tex]
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
[tex]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[/tex]
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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