Question

Determine if the given functions are inverse functions.
f(n) = (-16+n)/4
g(n) = 4n+16

Answer 1

The given functions
`\( f(n) = (-16 + n)/(4) \) and \( g(n) = 4n + 16 \)`are inverse functions.

Step-by-step explanation:

To determine if two functions are inverses, we need to check if
`\( f(g(n)) = n \) and \( g(f(n)) = n \). Let's evaluate \( f(g(n)) \) and \( g(f(n)) \)`for the given functions:

1. Evaluate \( f(g(n)) \):

`\[ f(g(n)) = f(4n + 16) = (-16 + (4n + 16))/(4) = (-16 + 4n + 16)/(4) = (4n)/(4) = n \]`

2. Evaluate \( g(f(n)) \):

`\[ g(f(n)) = g\left((-16 + n)/(4)\right) = 4\left((-16 + n)/(4)\right) + 16 = -16 + n + 16 = n \]`

Both \( f(g(n)) \) and \( g(f(n)) \) simplify to \( n \), confirming that these functions are inverses of each other. Therefore,
`\( f(n) = (-16 + n)/(4) \) and \( g(n) = 4n + 16 \)`are inverse functions.