Determine whether f(x)=5x+1/x and g(x)= x/5x+1 are inverse functions

Question

Determine whether f(x)=5x+1/x and g(x)= x/5x+1 are inverse functions. Explain how you know.

Answer 1

Find f(g(x)) and g(f(x)). If they both equal x, then they are inverses:

Answer 2

If f(x) and g(x) were inverse functions, then if f(a) = b, then g(b) = a

f(x) = (5x+1) / x g(x) = x / (5x+1)

f(1) = 6, but g(6) = 6/31 ≠ 1

So, f(x) and g(x) are NOT inverse functions.

Note: f(x) and g(x) are reciprocals of each other,