MathDB

The following functions are written on the board,

F(x) = x^2 + \frac{12}{x^2}, G(x) = \sin(\pi x^2), H(x) = 1.

If functions

f,g

are currently on the board, we may write on the board the functions

f(x) + g(x), f(x) - g(x), f(x)g(x), cf(x)

(the last for any real number

c

). Can a function

h(x)

appear on the board such that

|h(x) - x| < \frac{1}{3}

for all

x \in [1,10]

Problem Statement