Question

Given that functions f and g are each defined by f(x) = x + 2 and g(x) = 1 + 4, find the composite functions f ∘ g and g ∘ f

Answer 1

To find the composite functions f ∘ g and g ∘ f for the given functions f(x) = x + 2 and g(x), we substitute one function into the other. Assuming g(x) is correctly meant to be x + 4, both composite functions result in x + 6 after substitution and simplification.

Step-by-step explanation:

Composite Functions f ∘ g and g ∘ f Explained

When dealing with composite functions such as f ∘ g and g ∘ f, it's important to understand that these represent functions composed with each other. For the functions given, f(x) = x + 2 and g(x) = 1 + 4, we want to substitute the entire expression for g(x) into f(x) for f ∘ g, and vice versa for g ∘ f.

For f ∘ g, we calculate as follows:

This results in f(g(x)) = (x + 4) + 2.

Finally, simplify to g(f(x)) = x + 6.

In this case, both composite functions result in x + 6, assuming there was a typo in g(x).