# Math Help - Advanced Calc (Properties of Continuous Functions)

1. ## Advanced Calc (Properties of Continuous Functions)

Suppose that f: [a, b][a,b] is continuous. Prove that there is at least one fixed point in[a, b] - that is, x such that f(x)=x.

2. Originally Posted by lacy1104
Suppose that f: [a, b][a,b] is continuous. Prove that there is at least one fixed point in[a, b] - that is, x such that f(x)=x.
Hint: Define $g(x) = f(x) - x$. Now use intermediate value theorem to show $g$ has a zero on $[a,b]$.