Question

If f is continuous on [-1, 1] and f(-1) = 4 and f(1) = 3, then there exists a number r such that |r| < 1 and f(r) = π. Can this be true or false?

Please and thank you

Answer 1

The intermediate value theorem states that a function f(x) continuous on the interval [a,b] takes on every value between f(a) and f(b).

In the given case, a=-1, b=1, f(a)=4, and f(b)=3. π=3.14159.... lies between 4 and 3.

Therefore the statement "there exists a number r such that |r| < 1 and f(r) = π" is ______.


See also your previous question:
http://www.jiskha.com/display.cgi?id=1287182780