let f defined and continuous function in [ a , b ] with [ a , b

Bailee Short

Bailee Short

Answered question

2022-06-15

let f defined and continuous function in [ a , b ] with [ a , b ] f ( [ a , b ] ).Prove that f ( x ) = x admits at least one solution in [ a , b ]

I am not sure how to deal with this theorem so I have no idea where to start. if someone could walk me through the process that would be great.

Answer & Explanation

Jayce Bates

Jayce Bates

Beginner2022-06-16Added 18 answers

Let g ( x ) = f ( x ) x. Show that g is continuous (so the Intermediate Value Theorem applies to g), and that g ( a ) 0, and g ( b ) 0, and then...?

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