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Question 1196268: If  and f(x) is the inverse of g(x), determine the value of f(-1).
Sidenote: If you could also explain to me what the inverse of a function means and what it implies for this question specifically, I would really appreciate that :) thank you so much!!
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! You can look for the explanation in your book. Expecting f to be the inverse of g, then  -------------now just solve this for f(x).
Answer by ikleyn(52798)  (Show Source):
You can put this solution on YOUR website! .
About inverse function, read and learn from your textbook, or,
if you do not have it, then from this Wikipedia article
https://en.wikipedia.org/wiki/Inverse_function
Simply saying, the problem wants you find x such that
 = -1.
To solve this equation, multiply both sides by (6x+5), riding off the denominator. You will get
11-x = (-1)*(6x+5).
Simplify and find x
11 - x = -6x - 5
6x - x = -5 - 11
5x = -16
x =  .
ANSWER. x = .
CHECK.  =  =  =  = -1. ! Correct !
Solved.
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Notice, and it is IMPORTANT, that for solving this (and many other similar problems)
you do not need to seek for an explicit formula for the inverse function.
Your question is about a local value of an inverse function,
and in such cases the solution of the direct equation is just enough.
It is a MAJOR trick and a MAJOR lesson to learn from my post and to apply it in many other similar problems.
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