4. Prove that if f : [0, 1] → R is increasing (i.e., Vx, y Є [0, 1] x ≤ y ⇒ f(x) ≤ f(y)) and satisfies the Intermediate Value Property, then it is continuous.
4. Prove that if f : [0, 1] → R is increasing (i.e., Vx, y Є [0, 1] x ≤ y ⇒ f(x) ≤ f(y)) and satisfies the Intermediate Value Property, then it is continuous.
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![4. Prove that if f : [0, 1] → R is increasing (i.e., Vx, y Є [0, 1] x ≤ y ⇒ f(x) ≤
f(y)) and satisfies the Intermediate Value Property, then it is continuous.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93872b10-987f-4598-bc8e-fd6759803566%2Fede49da0-cacf-4de7-afe2-b6ee61eb0c03%2Fdv9q5v8d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Prove that if f : [0, 1] → R is increasing (i.e., Vx, y Є [0, 1] x ≤ y ⇒ f(x) ≤
f(y)) and satisfies the Intermediate Value Property, then it is continuous.
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