Let f : R → R be a function defined byf (x) = x +  , then f is

A function f:R→R defined by f(x)=2x is

Problem 2. Let A = {an : n ∈ N} = {a1, a2, . . . } be an infinite subset of R, and supposethat no element of A is listed twice: an 6 = am for all n 6 = m. This implies that the functionf : R → R defined byf (x) ={ 1n if x = an for some n ∈ N,0 if x /∈ A,is actually a function (but you do not need to prove this). Prove that limx→x0f (x) = 0 for anyx0 ∈ R.

If f(a)=f(b) implies that a = b then f is

Problem 4. Define the function f : R → R by f (x) = max{0, x}. For each a ∈ R, determineif f is differentiable at a and prove your answer

Fie functia f : R −→ R, definita prin f (x) = x + 1, ∀x ∈ R. Sa se rezolve ecuatia(f ◦ f )(x) = f 2(x).