(c) Suppose that f : [-1,1] →R is a continuous function such that r²+ f(x)² = 1 for every rE[-1, 1]. Prove that either f(r) = V1- r² for every z E [-1, 1], or else f(r) = -V1- r2 for every r E(-1, 1].
(c) Suppose that f : [-1,1] →R is a continuous function such that r²+ f(x)² = 1 for every rE[-1, 1]. Prove that either f(r) = V1- r² for every z E [-1, 1], or else f(r) = -V1- r2 for every r E(-1, 1].
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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![(c) Suppose that f : [-1,1] → R is a continuous function such that x2 + f(x)² = 1 for every
x € [-1, 1]. Prove that either f(x) = /1 – x² for every r E [-1, 1], or else f(x) = -/1- x²
for every r E [-1, 1].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb171a314-9915-4efd-81f0-27717f1f1f89%2Fbad260e1-9bf2-4ba5-bd82-2910e4df31db%2Fhhhdkdg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(c) Suppose that f : [-1,1] → R is a continuous function such that x2 + f(x)² = 1 for every
x € [-1, 1]. Prove that either f(x) = /1 – x² for every r E [-1, 1], or else f(x) = -/1- x²
for every r E [-1, 1].
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