Question

1st Option: Everywhere on U or Everywhere on

interior of U or There is at least one point in
the interior of U where they are not linearly independent
2nd Option: G is injective on all of U or G is
no

Answer 1

The question is asking about the conditions for a function to be injective on a set.

Step-by-step explanation:

The question seems to be asking about the conditions under which a function G is injective (or one-to-one) on a set U. The options given are a bit unclear, but I will provide a step-by-step explanation of how to interpret them.

1. Everywhere on U or Everywhere on the interior of U or There is at least one point in the interior of U where they are not linearly independent. These options seem to be more appropriate for linearly independent vectors, not functions. So, we can disregard them.
2. G is injective on all of U, or G is non-injective on at least one point in the interior of U. These options are more appropriate for injectivity. If G is injective on all of U, it means that distinct points in U always have distinct images under G, which implies one-to-one correspondence. If G is non-injective on at least one point in the interior of U, it means that there exists at least one pair of distinct points whose images are the same, which violates the one-to-one correspondence property.

Therefore, the second option is the correct interpretation for determining if a function G is injective on a set U.