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

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

Mathematics
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\[\large f(x) = 6(x + 2) - 3\] 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'?
Find inverse of f(x) first put f(x) = y y = 6(x+2) - 3 thus inverse will be \[ \frac{ y-3 }{ 6 } -2 = x\] Now x = 21 then find y

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sorry its y + 3
wait, why isn't it (y+2)/6 -3 ?
I'm just curious
We 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
okay thanks :) so y = 125, right?
\[y = \frac{ 14 }{ 6 } \]
how did you get that? I did: 21 = (y+3)/6 -2 126 = y + 1 125 = y
\[y = \frac{ x+3 }{ 6 } - 2\] \[y = \frac{ 21+3 }{ 6 } - 2\] \[y = \frac{ 26 }{ 6 } - 2\] \[y = \frac{ 26 - 12 }{ 6 } \]
I mentioned in explanation that I forgot mentioning the last part. Sorry
http://www.purplemath.com/modules/invrsfcn3.htm i hope this helps
just plug in 21 for f(x)
instead of going through all complex steps
when I just plugged in 21 for f(x), I got 2, not 14/6. Did I do something wrong?
^You did it correctly @RosieF There was a typo in the response up there
okay :) thank you everyone that helped :)
inverse of a linear function. For a linear function f(x), find \({\rm f}^{-1}(a)\) \(\large\color{black}{ \displaystyle f(x)=mx+b }\) \(\large\color{black}{ \displaystyle y=mx+b }\) \(\large\color{black}{ \displaystyle x=my+b }\) \(\large\color{black}{ \displaystyle x-b=my }\) \(\large\color{black}{ \displaystyle y=(x-b )/m }\) \(\large\color{black}{ \displaystyle y=(a-b )/m }\) \(\large\color{black}{ \displaystyle f^{-1}(a)=(a-b )/m }\) or, going with a trick: \(\large\color{black}{ \displaystyle f(x)=mx+b }\) \(\large\color{black}{ \displaystyle a=mx+b }\) \(\large\color{black}{ \displaystyle a-b=mx }\) \(\large\color{black}{ \displaystyle (a-b)/m=x }\) (don't forget x is the inverse function) \(\large\color{black}{ \displaystyle (a-b)/m={\rm f}^{-1}(a) }\)
so you can see it is all the same thing
thank you for explaining how the trick works @SolomonZelman

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