Question

Which two functions are inverses of each other?

a) f(x) = x, g(x) = -x
b) f(x) = -2x, g(x) = -x
c) f(x) = -4x, g(x) = +x
d) f(x) = -8x, g(x) = 8x

Answer 1

The correct answer is a) f(x) = x, g(x) = -x. To find the inverse of a function, we switch the x and y variables and solve for y. These functions are inverses of each other because f(g(x)) = x and g(f(x)) = x for all x.

Step-by-step explanation:

The correct answer is a) f(x) = x, g(x) = -x.

To find the inverse of a function, we switch the x and y variables and solve for y. In this case, if we let y = f(x) = x, then the inverse function is g(x) = -x. We can verify that these functions are inverses of each other by plugging in values for x and seeing that the outputs are the same.

For example, if we choose x = 2, then f(2) = 2 and g(2) = -2. Similarly, if we choose x = -3, then f(-3) = -3 and g(-3) = 3. Since f(g(x)) = x and g(f(x)) = x for all x, we can conclude that f(x) = x and g(x) = -x are inverse functions.