Suppose that f,g:[a,b]->R are continuous functions with f(a)<g(a) and f(b)>g(b). Prove that there exists an x in (a,b) with f(x)=g(x). I believe this uses the Intermediate Value Theorem.

Antwan Perez

Antwan Perez

Answered question

2022-10-21

Suppose that f , g : [ a , b ] R are continuous functions with f ( a ) < g ( a ) and f ( b ) > g ( b ). Prove that there exists an x ( a , b ) with f ( x ) = g ( x ). I believe this uses the Intermediate Value Theorem.

Answer & Explanation

megagoalai

megagoalai

Beginner2022-10-22Added 22 answers

Hint: What can you say about h : [ a , b ] R , given by h ( x ) = f ( x ) g ( x )?
Alessandra Cummings

Alessandra Cummings

Beginner2022-10-23Added 1 answers

h is continuous, i guess

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