1. The problem statement, all variables and given/known data The following function f is a function from R to R. Determine whether f is injective (one-to-one), surjective (onto), or both. Please give reasons. 2. Relevant equations f(x) = (x+1)/(x+2) if x != -2 f(x) = 1 when x = 2 3. The attempt at a solution f'(x) = 1/(x+2)2 > 0 for all x and the limits at both infinities are 1 using l'hopital. So the way I see it is the function grows from 1+ when x is a large negative, and then theres a horizontal assymptote at x = -2 so just before x = -2 f(x) tends to infinity and just after x = -2 the f(x) goes from negative infinity and gradually increases to 1. and then ofcourse at the point x = - 2 f(x) = 1 because that value has been forced in the definition. So now by visualising the graph I have a strong suspicion that this function is bijective, but I have no idea how to prove it 'analytically'