Problem 535 (difficulty: 3/10)

Let \(\displaystyle f:[0,1] \to [0,1]\) and \(\displaystyle g:[0,1] \to [0,1]\) be continuous and \(\displaystyle f(0)\geq g(0)\), \(\displaystyle f(1)\leq g(1)\). Prove that there exists an \(\displaystyle x\in [0,1]\), such that \(\displaystyle f(x)=g(x)\).

Give me another random problem!