List of top Mathematics Questions on Functions asked in AP EAPCET

Let f : ℝ → ℝ be a function such that:

|f(x) − f(y)| ≤ ½ |x − y|, for all x, y ∈ ℝ 

f′(x) ≥ ½, for all x ∈ ℝ, and f(1) = ½

Find the number of points of intersection of the curves:

y = f(x) and y = x² − 2x − 5