Question

Determine whether f(x) = 5x+1/x and g(x)= x/ 5x+1 are inverse functions explain how you know. please explain in steps or worded responses if possible thank you so much :D

Answer 1

Hello from MrBillDoesMath!

Answer:

No

Discussion:

If the functions are inverses, then f(g(x)) = x  for appropriate x. Consider x = 1.

g(1) = 1/ (5(1) + 1) = 1/6

f(g(1)) = f (1/6) =  5(1/6) + 1/ (1/6) = 5/6 + 6 = 6 5/6   <> 1

Conclusion: f(g(1)) <> 1 so the functions are not inverses

Thank you,

MrB