Round-Trip Theorum
How are you supposed to use the Round-Trip Theorum in problem 3.7.25?
posted by Monica Moore at 4:13 PM
Blog for students in Mr. Karafiol's Period 4 Precalculus BC class to talk about math, learning math, etc.
posted by Monica Moore at 4:13 PM
3 Comments:
The Round Trip Theroem basically says that if a one-to-one function [f(x)] has an inverse function [g(x)], then two things should be true. One: f(g(x))=x, for every x in g's domain. Two: g(f(x))=x for every x in f's domain.
So for Number 25, you have to show that g is the inverse of f by proving the f(g(x))=x and g(f(x))=x. Since f(x)=1/(x+1) and g(x)=(1-x)/x, g(f(x))= (1-(1/(x+1)))/(1/(x+1)). (I know that's a lot of parentheses, by if you simplify by hand or by using your calculator, it should equal x!)
Do the same thing to simplify f(g(x)) and you've used the Round Trip Theorem to prove that g is the inverse of f!
thanks
Right on, Casey Blue!
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