- #1
louie3006
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Homework Statement
:discuss continuity of the composite function h(x)=f(g(x)) when A} F(x)=X^2 , g(x) = x-1
B} f(x) = 1/x-6 , g(x) = X^2+5
where should I start ?
Please use parentheses.louie3006 said:when x = -6, that would make f(x) = 1/x-6 discontinuous right?
A composite function is a function that is formed by combining two or more functions in a specific order. The output of one function becomes the input of another function, resulting in a new function.
In a composite function, continuity is defined as the property of the function where the limit of the function at a given point is equal to the value of the function at that point. This means that there are no abrupt changes or breaks in the function.
The continuity of a composite function is important because it ensures that the function is well-defined and smooth. This means that the function can be graphed and analyzed without any interruptions or gaps, making it easier to understand and work with.
To determine the continuity of a composite function, you can use the continuity rules for composite functions. These rules state that if both individual functions are continuous at a given point, then the composite function is also continuous at that point.
If one of the functions in a composite function is not continuous, then the entire composite function will also not be continuous at that point. This means that there will be a break or discontinuity in the function, which can affect the overall behavior and analysis of the function.