Question

Which pair of functions are inverses of each other?

A. f(x) = 5/x - 2 and g(x) = x + 2/5
B. f(x) = 7x-2 and g(x) = x - 2/7
C. f(x) = x/5+ 6 and g(x) = 5x - 6
D. f(x) = ∛x/6 and g(x) = 6x³

Answer 1

The pair of functions that are inverses of each other are A. f(x) = 5/x - 2 and g(x) = x + 2/5.

Step-by-step explanation:

The pair of functions that are inverses of each other are A. f(x) = 5/x - 2 and g(x) = x + 2/5.

To show that these functions are inverses, we need to demonstrate that when f(x) is applied to g(x), and vice versa, we get back the original value of x.

Let's start by applying f(x) to g(x):

f(g(x)) = f(x + 2/5)

= 5 / (x + 2/5) - 2

= (5x + 2) / (5(x + 2/5)) - 2

= (5x + 2) / (5x + 2) - 2 = 1 - 2 = -1.

Now let's apply g(x) to f(x):

g(f(x)) = g(5/x - 2)

= 5/(5/x - 2) + 2/5

= 5x/(5 - 2x) + 2/5

= (5x + 2) / (5 - 2x) = 1 - 2x / (5 - 2x) = 1.

Since f(g(x)) = -1 and g(f(x)) = 1, we can conclude that f(x) and g(x) are inverses of each other.