Answer to Question #5975 in Calculus for Samantha

Question #5975
Let f(x)=x/(x-6). Find a function y=g(x) so that (f*g)(x)=x.
Expert's answer
In this task we’re dealing with composition of functions. Recall the definition: function composition is the application of one function to the results of another. We need to find such function g(x) so that function f applied to it will give juxt x.

Due to the statement of the question f(x) = x/(x - 6)

To obtain function composition (f*g)(x)=f(g(x)) we have to substitute g(x) instead of x into the expression for

as f(x) = x/(x - 6)

we have (f*g)(x) = f(g(x)) = g(x)/[g(x) - 6].

And the last expression has to be equal to x:

g(x)/[g(x) - 6]=x


g(x) = xg(x) - 6x, so (x - 1)g(x) = 6x, and g(x) = 6x/(x - 1). Thus, g(x) is the inverse of f(x).

Dear Samantha
For you and other our visitors we created this video. Please take a look !

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!


No comments. Be first!

Leave a comment

Ask Your question

New on Blog