SOLUTION: Find g^-1(x) if g(x)= -4x/6x+1

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Question 22122: Find g^-1(x) if g(x)= -4x/6x+1
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
i assume you mean g(x) = -4x%2F%286x%2B1%29 ?

ok, inverses...you have y=-4x%2F%286x%2B1%29. All it is asking for is x=? How do to this? by re-arranging...

y+=+-4x%2F%286x%2B1%29
y%286x%2B1%29+=+-4x
6xy%2By+=+-4x
6xy+%2B+4x+=+-y
x%286y+%2B+4%29+=+-y
x+=+-y%2F%286y+%2B+4%29

so g(y) = -y%2F%286y+%2B+4%29

However, we tend to write equations in terms of x rather than y, so this is g(x) = -x%2F%286x+%2B+4%29

And this is the inverse of our original function, so we have g%5E%28-1%29%28x%29+=+-x%2F%286x+%2B+4%29
jon.