anonymous
  • anonymous
if f(x)=-5x-13 than f^-1(x)=?
Mathematics
chestercat
  • chestercat
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freckles
  • freckles
the first step is to solve y=-5x-13 for x.
freckles
  • freckles
For example, I bet you know how to solve 5=-5x-13 for x. You would add 13 on both sides right? 5+13=-5x then divide both sides by -5 (5+13)/(-5)=x just do the same thing here but instead of 5 you have y
anonymous
  • anonymous
I would add 13 to both sides and divide both sides by -5 which i guess would leave me with 5=x

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anonymous
  • anonymous
I don't understand how to do the same with y though
jim_thompson5910
  • jim_thompson5910
|dw:1436928354040:dw|
jim_thompson5910
  • jim_thompson5910
first add 13 to both sides |dw:1436928386487:dw|
jim_thompson5910
  • jim_thompson5910
that is done to cancel out the '-13' on the right side |dw:1436928424337:dw| since -13 and +13 add to 0. The 0 goes away
jim_thompson5910
  • jim_thompson5910
after adding 13 to both sides, we now have y+13 = -5x with me so far?
anonymous
  • anonymous
so far yes
jim_thompson5910
  • jim_thompson5910
|dw:1436928497040:dw|
jim_thompson5910
  • jim_thompson5910
the next step is to undo the "-5 times x" so we divide both sides by -5 which will isolate x |dw:1436928547068:dw|
jim_thompson5910
  • jim_thompson5910
-5 divided by itself gives 1 1 times x = x, so the '1' goes away leaving just x behind |dw:1436928578962:dw|
jim_thompson5910
  • jim_thompson5910
once we get \[\Large x = \frac{y+13}{-5}\] we swap x and y to get \[\Large y = \frac{x+13}{-5}\] and this is the inverse. We can write that inverse as \[\Large f^{-1}(x) = \frac{x+13}{-5}\]
anonymous
  • anonymous
Thank you for your help
jim_thompson5910
  • jim_thompson5910
you're welcome

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