State whether each of the following functions f have a well-defined inverse or not. Recall that a function has an inverse if, fo
r every element in the codomain, there exists exactly one element in the domain that maps to it; that is, the function is onto (surjective) and one-to-one (injective). If it does, provide the inverse function f −1 . If it does not, explain if it violates the onto condition, one-on-one condition, or both, and justify your response. (a) f : R → R, f(x) = 3x−12 (b) f : R → R, f(x) = x 2 +1 (c) f : R → R, f(x) = 3x 3 −12x (d) f : R + → R +, f(x) = √ x+1, where R + denotes the positive reals
