Let f: [-a, a] → \(\mathbb R\) be continuous and differentiable function such that f'(x) ≤ 1 for all x ∈ (-a, a). If f(a) = a and f(-a) = -a then
1
f(x) = x ∀ x ∈ (-a, a)
2
f(x) = x2 ∀ x ∈ (-a, a)
3
f(x) = sin x ∀ x ∈ (-a, a)
4
f(x) = - x ∀ x ∈ (-a, a)