Explanation The algebraic combinations of continuous functions are continuous at every point at which all the functions involved are defined. That means the sums, differences, constant multiples, products, quotients, and powers of continuous functions are continuous were defined. The polynomials and rational functions of two variables are continuous at every point at which they are defined. If the function f is continuous at ( x 0 , y 0 ) and g is a single-variable function continuous at f ( x 0 , y 0 ) , then the composition h = g ∘ f defined by h ( x , y )

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Chapter 14, Problem 6GYR

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Provide notes on algebraic combinations and compositions of continuous functions.

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