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The domain of the function [tex]f(x)= \dfrac{(x+1)}{(x^2-6x+8)}[/tex] will not be defined at points 2 and 4.
What is the domain and range of a function?
The domain is the set of values for which the given function is defined.
The range is the set of all values which the given function can output.
In order to find the domain of the function [tex]f(x)= \dfrac{(x+1)}{(x^2-6x+8)}[/tex], we need to equate the denominator of the function with 0, and the value of x will be the value at which the domain is not defined, therefore, the equation can be written as,
[tex]x^2-6x+8 = 0\\\\x^2 -4x-2x+8=0\\\\x(x-4) - 2(x-4)=0\\\\(x-2)(x-4)=0[/tex]
Equating each of the factor with 0, we get x = 2 and x = 4.
Hence, the domain of the function [tex]f(x)= \dfrac{(x+1)}{(x^2-6x+8)}[/tex] will not be defined at points 2 and 4.
Learn more about Domain:
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