State if the given functions are inverses. F(n)= -5+5/3n, g(n)= 3/5n+3 (n's are on the side of the fraction) State if the given functions are inverses.

Question

Please guide me through this. 

Answer 1

No problem, Malik.  Thanks for the clarification. If two functions f(x) and g(x) are inverses then f(g(x)) and g(f(x)) should both evaluate to x.

 

F(g(n)) = -5 + 5/3 * [(3/5) n + 3] = -5 + n + 5 = n

g(F(n)) = 3/5 * [-5 + (5/3) n] + 3 = -3 + n + 3 = n

 

Hence, these two functions are inverses of each other.

Answer 2

Malik,

 

Choose any number, 1 is easy to work with, plug it into the F(x) function, get the answer.   Plug this answer into the g(x) function.  See if you get 1 for your answer.  If you do, then the functions are inverses.

 

If two functions are inverses, then their ordered pairs would appear as:

 

(x,y)  and the inverse would be (y,x)

 

Inverses always have their coordinates switched with the x's and y's, easy to tell if they are inverses or not.