How to tell if a function is inverse

Question

F(n)=1-1/4n

h(n)=-4n+4

Answer 1

To find out if two functions are inverses of each other, perform the functions on each other.  If both results are the original variable (in your case n), then the functions are inverse.

For your functions to be inverses, you need to have the results F(h(n)) = n and h(F(n)) = n.

F(h(n))

F(-4n + 4)

1 - 1/4(-4n + 4)

1 - (-n + 1)

1 + n - 1

n

The check worked for F(h(n)), but we still have to check h(F(n))

h(F(n))

h(1 - 1/4n)

-4(1 - 1/4n) + 4

-4 + n + 4

n

Since both F(h(n)) = 0 and h(F(n)) = 0, the functions are inverses.