Function aligns value from one set to another. The function will have a removable discontinuity at x = -3.
What is Function?
A function assigns the value of each element of one set to the other specific element of another set.
As the function is given to us,
[tex]F(x) = \dfrac{(x^2+12x+27)}{(x^2+4x+3)}[/tex]
Now, factorizing the numerator and the denominator,
[tex]F(x)=\dfrac{(x+3)(x+9)}{(x+3)(x+1)}[/tex]
Now, in order to find the point at which the function will be discontinued, we will equate the denominator with 0.
[tex](x+3)(x+1)=0\\\\\\(x+3)=0\\x =-3\\\\\\(x+1)=0\\x=-1[/tex]
Now, As (x+3) is the factor of the numerator and the denominator, therefore, you will have a removable discontinuity, which appears as a hole in the graph.
Hence, the function will have a removable discontinuity at x = -3.
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