46. Prove that there is no continuous function f: R→ R such that, for each c E R, the equation f(x) = c has exactly two solutions.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.4: Related Rates
Problem 4E: Assume x and y are functions of t. Evaluate dydtfor each of the following. 4x36xy2+3y2=228;...
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46. Prove that there is no continuous function f: R→R such that, for each c ER, the equation
f(x) = c has exactly two solutions.
Transcribed Image Text:46. Prove that there is no continuous function f: R→R such that, for each c ER, the equation f(x) = c has exactly two solutions.
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