1. ## Composite Functions

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.

Did i do this right?
Thanks.

2. Originally Posted by Såxon
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.

Did i do this right?
Thanks.

Sounds fine to me. Only stress that c is ANY real point, and thus h(x) is continuous everywhere.

Tonio