The function [tex]f[/tex] is continuous where [tex]f(-5)=-3[/tex] and [tex]f(5)=-1[/tex], and [tex]g[/tex] is a function defined by [tex]g(x)=1-(f(x))^{2}[/tex]. Is there a value [tex]c[/tex] for [tex]-5\leq c\leq 5[/tex] such that [tex]g(c)=1[/tex]? Why, or why not?
A. Yes; the function [tex]g[/tex] is continuous
B. No; 1 is not between [tex]g(-5)[/tex] and [tex]g(5)[/tex], so IVT cannot guarantee there is a value [tex]c[/tex] for [tex]-5\leq c \leq 5[/tex] such that [tex]g(c)=1[/tex]
C. No; the function [tex]g[/tex] is not continuous