Question

Which functions are the same as their inverse functions?

A) f(x) = 1 + 5, , -5
B) g(x) = 1/x + 2
C) h(x) = 1 - 1/3x
D) k(x) = 1/1 + x, , -1

Answer 1

The function that is the same as its inverse function is called an even function.

Step-by-step explanation:

The function that is the same as its inverse function is called an even function. An even function is symmetric with respect to the y-axis, which means that if you reflect the graph of the function about the y-axis, it matches the original function. In other words, if f(x) = f(-x), then f(x) is an even function and its inverse function is also f(x).

Out of the options provided, only option A) f(x) = 1 + 5 is an even function because it remains the same when you substitute -x for x. Therefore, option A) is the only function that is the same as its inverse function.