Question

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

Answer 1

inverse means opposite.. If I have this right the inverse should be more something like g(x)= -5x-1x... the g(x) example seems more like a commutative function, because it seems to have changed the order of the x that was behind 1... (again not sure if I am right, but I hope this helps :)

Answer 2

g(x) is not inverse of f(x)

Explanation:

We have

`f(x)=(5x+1)/(x)\\\\f(x)=5+(1)/(x)\\\\(1)/(x)=f(x)-5\\\\x=(1)/(f(x)-5)\\\\f^(-1)(x)=(1)/(x-5)`

Hence inverse of f⁻¹(x) = 1/(x-5) which is not equal to g(x), so g(x) is not inverse of f(x).