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

Answer:

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

Step-by-step explanation:

We have

             $f(x)=\frac{5x+1}{x}\\\\f(x)=5+\frac{1}{x}\\\\\frac{1}{x}=f(x)-5\\\\x=\frac{1}{f(x)-5}\\\\f^{-1}(x)=\frac{1}{x-5}$

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).