Use the concept of composite functions to explain why h(x) = |x^2 - 4x - 6| is a continuous function.
g(x) = |x|
f(x) = x^2 - 4x - 6
These are both continuous, f because of the properties of continuous functions, the absolute value of g is continues too, so the composite is continuous. If f is continuous at c and g is continuous at f(c), then the composite g o f is continuous at c.
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Thanks.