Question: Suppose f is a continuous function on [-2,2] such that f(-2)=1 and f(2)=-1. Which of the properties below follow without further restriction on f by

Suppose f is a continuous function on [-2,2] such that f(-2)=1 and f(2)=-1.

Which of the properties below follow without further restriction on f by applying the Intermediate Value Theorem?

a) f(x)+1>=0 on (-1,2)

b) f^2(c)= 1/4 for some c in (-2,2)

c) f(c)=0 for some c in (-1,1)

Please explain how you got answer so that I can understand it. I believe b and c are true but don't know about a. Please help.

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