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anonymous
 one year ago
PLEASE HELP!!!
Given the function f(x) = 6(x+2) − 3, solve for the inverse function when x = 21.
anonymous
 one year ago
PLEASE HELP!!! Given the function f(x) = 6(x+2) − 3, solve for the inverse function when x = 21.

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johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.0\[\large f(x) = 6(x + 2)  3\] Let's rewrite this as \[\large y = 6(x + 2)  3\] To find the inverse of a function...we switch the 'x' and the 'y' and then solve again for 'y' \[\large y = 6(x + 2)  3\] turns into \[\large x = 6(y + 2)  3\] Now how would we solve that for 'y'?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Find inverse of f(x) first put f(x) = y y = 6(x+2)  3 thus inverse will be \[ \frac{ y3 }{ 6 } 2 = x\] Now x = 21 then find y

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wait, why isn't it (y+2)/6 3 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0We have to find inverse of x. so simply putting y in position of x wont give us that. we assume that our function = y thus y = 6(x+2)  3 now whats x in terms of y? x = y+3/6 2  (1) thats our inverse function BUT its not the answer yet. our f(x) = y thus f(x)^1 = y now we change position of x and y thus getting, y = x+3/6  2 sorry missed last part in above comments

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay thanks :) so y = 125, right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[y = \frac{ 14 }{ 6 } \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how did you get that? I did: 21 = (y+3)/6 2 126 = y + 1 125 = y

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[y = \frac{ x+3 }{ 6 }  2\] \[y = \frac{ 21+3 }{ 6 }  2\] \[y = \frac{ 26 }{ 6 }  2\] \[y = \frac{ 26  12 }{ 6 } \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I mentioned in explanation that I forgot mentioning the last part. Sorry

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0http://www.purplemath.com/modules/invrsfcn3.htm i hope this helps

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2just plug in 21 for f(x)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2instead of going through all complex steps

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0when I just plugged in 21 for f(x), I got 2, not 14/6. Did I do something wrong?

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.0^You did it correctly @RosieF There was a typo in the response up there

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay :) thank you everyone that helped :)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2inverse of a linear function. For a linear function f(x), find \({\rm f}^{1}(a)\) \(\large\color{black}{ \displaystyle f(x)=mx+b }\) \(\large\color{black}{ \displaystyle y=mx+b }\) \(\large\color{black}{ \displaystyle x=my+b }\) \(\large\color{black}{ \displaystyle xb=my }\) \(\large\color{black}{ \displaystyle y=(xb )/m }\) \(\large\color{black}{ \displaystyle y=(ab )/m }\) \(\large\color{black}{ \displaystyle f^{1}(a)=(ab )/m }\) or, going with a trick: \(\large\color{black}{ \displaystyle f(x)=mx+b }\) \(\large\color{black}{ \displaystyle a=mx+b }\) \(\large\color{black}{ \displaystyle ab=mx }\) \(\large\color{black}{ \displaystyle (ab)/m=x }\) (don't forget x is the inverse function) \(\large\color{black}{ \displaystyle (ab)/m={\rm f}^{1}(a) }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2so you can see it is all the same thing

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank you for explaining how the trick works @SolomonZelman
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