Question

Which pair of functions are inverses of each other?

A. R(x) = 7x - 2 and g(x) = ***
B. f(x) = and g(x) = 6 x
C. f(x) = -2 and g(x) = 2
D. f(x) = 6 and g(x) = 5x - 6

Answer 1

The pair of functions that are inverses of each other are R(x) = 7x - 2 and g(x) = (x + 2)/7.

Step-by-step explanation:

Functions that are inverses of each other undo the effect of one another. In other words, if you apply one function and then apply the other, you get back to the original value. To find the inverse of a function, you switch the roles of x and y and solve for y.

For example, for the function R(x) = 7x - 2, the inverse would be found by swapping x and y: x = 7y - 2. Solving for y gives y = (x + 2)/7, which is the inverse function.

Looking at the options provided, (A) R(x) = 7x - 2 and g(x) = (x + 2)/7 are inverses of each other.