Question

If f and g are injective functions, so is ________?

1) f + g
2) f - g
3) f * g
4) f / g

Answer 1

If f and g are injective functions, then f divided by g will also be an injective function.

Step-by-step explanation:

If f and g are injective functions, then the operations of addition, subtraction, and multiplication do not necessarily preserve injectivity. However, when it comes to division, if g is an injective function, then the composition f / g is also injective.

To prove that f / g is injective, we can assume that f(x) / g(x) = f(y) / g(y) for some x and y in the domain of f. Since g is injective, we know that g(x) = g(y). Multiplying both sides of the equation by g(x), we get f(x) = f(y). And since f is injective, it follows that x = y. Therefore, f / g is injective.