Show that f and g are inverses of each other by verifying that f(g(x))=x=g(f(x)). f(x)= 1/x; g(x)=1/x

Question

basic concepts 

Answer 1

Gabrielle, 

There are two ways in which you can actually approach this problem. The first method is the algebraic way.

 

Since through what I have shown about an inverse function that it is an inverse of f(x) where f(g(x))=x, then from this principle, in order to find the inverse function, you must first switch the values of f(x) with x in the equation.

 

f(x) = (1/x)

 

x = (1/f(x))

 

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

 

Another method that you can use in order to understand this relationship is (if you have graphing calculator that also does have graphic design features) to graph both graphs on the equation and then see how the x and y values of both graphs reflects on one another. When you look at both g(x) and f(x), they are not only the same function with one another but they are also have values that corresponds with the accepted principle of an inverse function f(g(x))=x=g(f(x))

 

Please let me know if you still have any questions by messaging me on Wyzant. Thanks

Andy L.

Answer 2

Obviously true since f(g(x)) would be the taking of the reciprocal of 1/x, which indeed is x.  & vice versa.