To determine if a function is injective, we need to check if each input value maps to a unique output value. If the function f(x) = x^2 is defined on the set of real numbers, then it is not injective because multiple input values (e.g. 2 and -2) map to the same output value (4). Therefore, the function f(x) = x^2 is not injective. **

One way to prove that function f is injective if function g is injective is to show that for any two distinct inputs x1 and x2, the outputs f(x1) and f(x2) are also distinct. Since g is injective, we know that g(x1) and g(x2) are distinct, and we can use this property to show that f is injective as well. Specifically, we can use the fact that g(f(x1)) = g(f(x2)) implies f(x1) = f(x2), and since g is injective, this implies x1 = x2. Therefore, f is injective. **

The savings bank may be blocking online banking customers for security reasons. They may have detected suspicious activity on certain accounts and are taking precautionary measures to protect their customers' funds and personal information. Additionally, the bank may be conducting routine maintenance or updates to their online banking system, temporarily restricting access to ensure a smooth and secure user experience once the maintenance is complete. It is also possible that there may be technical issues or glitches with the online banking platform that need to be resolved before customers can access their accounts again. **

Savings bank transactions can typically be deleted by accessing the account statement or transaction history on the bank's online portal or mobile app. From there, you can select the specific transaction you wish to delete and look for an option to remove or delete it. If you are unable to delete the transaction yourself, you can contact your bank's customer service for assistance in removing the transaction from your account history. It's important to note that some transactions may not be able to be deleted, especially if they are already processed or finalized. **

To show that if f and g are injective, then gf is also injective, we can use the definition of injective functions. An injective function is one where distinct inputs map to distinct outputs. So, if f and g are injective, then for any distinct inputs x1 and x2, f(x1) ≠ f(x2) and g(y1) ≠ g(y2) for any distinct outputs y1 and y2. Now, consider the composition gf. If gf(x1) = gf(x2), then f(x1) = f(x2), which implies x1 = x2 by the injectivity of f. Therefore, gf is also injective. **

To determine if a mapping is surjective or injective, we need to look at the properties of the mapping. Please provide the specific mapping you would like me to analyze. **

The first mapping is not injective because multiple elements in the domain map to the same element in the codomain. However, it is surjective because every element in the codomain is mapped to by an element in the domain. The second mapping is injective because each element in the domain maps to a unique element in the codomain. However, it is not surjective because not every element in the codomain is mapped to by an element in the domain. **

The first mapping is injective because each element in the domain is mapped to a unique element in the codomain. The second mapping is surjective because every element in the codomain is mapped to by at least one element in the domain. **