Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
Answer: f(x) = 3/x
==========================================================
Explanation:
If g(x) is the inverse of f(x), and vice versa, then we have these two properties:
- f(g(x)) = x
- g(f(x)) = x
Since we want to find a function that is its own inverse, we want f(x) and g(x) to be the same function.
Through trial and error, you should find that f(x) = g(x) = x fit the description.
f(x) = x
f( g(x) ) = g(x) ... replace every x with g(x)
f( g(x) ) = x
You should find that g(f(x)) = x as well.
One possible answer is f(x) = x
---------------------------
Through more trial and error, you should find that f(x) = g(x) = 1/x works as well. In fact, anything of the form f(x) = g(x) = k/x will work.
The proof can be written as follows
f(x) = k/x
f( g(x) ) = k/( g(x) )
f( g(x) ) = k/( k/x )
f( g(x) ) = (k/1) divide (k/x)
f( g(x) ) = (k/1) * (x/k)
f( g(x) ) = x
Through similar steps, you should find that g(f(x)) = x is the case also.
This proves that f(x) = k/x is its own inverse, where k is a real number constant.
Another possible answer is anything of the form f(x) = k/x
If we pick k = 3, then we get f(x) = 3/x which is the answer I wrote above.
You can pick any k value you want.
---------------------------
There may be other types of functions that have this property, but I'm blanking on what they might be.
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
