Let f, g : R → R be given functions. Suppose that f and g are continuous at c ∈ R.Prove that the functionl(x) := inf{f (x), g(x)}, x ∈ R,is continuous at c.

Question

Let f, g : R → R be given functions. Suppose that f and g are continuous at c ∈ R.Prove that the functionl(x) := inf{f (x), g(x)}, x ∈ R,is continuous at c.
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Solution 1

To prove that the function l(x) := inf{f(x), g(x)}, x ∈ R, is continuous at c, we need to show that for every ε > 0, there exists a δ > 0 such that for all x in R with |x - c| < δ, we have |l(x) - l(c)| < ε.

Let's start by noting that since f and g are continuous at c, for every ε > 0, there exist Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

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Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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