explain please.

Question

The function f is continuous where f(−5) = −1 and f(5) = 6, and g is a function defined by g(x) = 1 − (f(x))2. Is there a value c for −5 ≤ c ≤ 5 such that g(c) = 1? Why, or why not?

Answer 1

g(x) = 1-(f(x))^2, f(5) =6

g(f(5)) = g(6) = 1-36 = -35

f(-5) = -1

g(f(-5) = g(-1) = 1-1 = 0

-1 < g(c) < -35, which does not include any positive value such as +1

g(c) = (-35 -0)/(5- -5) = -3.5= 1-c^2

c^2=4.5

c=sqr4.5