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

1. anonymous

@sangya21 @tkhunny

2. johnweldon1993

$\large f(x) = 6(x + 2) - 3$ 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'?

3. anonymous

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

4. anonymous

sorry its y + 3

5. anonymous

wait, why isn't it (y+2)/6 -3 ?

6. anonymous

I'm just curious

7. anonymous

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

8. anonymous

okay thanks :) so y = 125, right?

9. anonymous

$y = \frac{ 14 }{ 6 }$

10. anonymous

how did you get that? I did: 21 = (y+3)/6 -2 126 = y + 1 125 = y

11. anonymous

$y = \frac{ x+3 }{ 6 } - 2$ $y = \frac{ 21+3 }{ 6 } - 2$ $y = \frac{ 26 }{ 6 } - 2$ $y = \frac{ 26 - 12 }{ 6 }$

12. anonymous

I mentioned in explanation that I forgot mentioning the last part. Sorry

13. anonymous

http://www.purplemath.com/modules/invrsfcn3.htm i hope this helps

14. SolomonZelman

just plug in 21 for f(x)

15. SolomonZelman

instead of going through all complex steps

16. anonymous

when I just plugged in 21 for f(x), I got 2, not 14/6. Did I do something wrong?

17. johnweldon1993

^You did it correctly @RosieF There was a typo in the response up there

18. anonymous

okay :) thank you everyone that helped :)

19. SolomonZelman

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) $$\large\color{black}{ \displaystyle (a-b)/m={\rm f}^{-1}(a) }$$

20. SolomonZelman

so you can see it is all the same thing

21. anonymous

thank you for explaining how the trick works @SolomonZelman