Answer:
First problem:
Limiting the Domain to [tex]x\leq 0[/tex] (option A in the list)
Second problem:
All the three statements are true, so pick option D)
Step-by-step explanation:
Recall that a function in order to have inverse needs to be a one-to-one function. In the case of the function they give you in the problem:
[tex]f(x)= 3x^2+1[/tex]
the graph corresponds to a parabola with vertex at x=0 and y=1 (0, 1), and since it has two branches that correspond to equal y-values for opposite pairs of x values, it doesn't satisfy the conditions for the existence of inverse. But if we limit the Domain of it considering just one half of the graph (for example limiting the Domain to the values to one side of the parabola's vertex, then this restricted function is one-to-one and we can find its inverse.
So the option of limiting the Domain to x-values smaller than or equal to zero, suggested in option A of the list of answers will do the job we need.
In the following problem, the three first statements are true for an inverse function, so pick option D that says that all previous statements are true.
