## anonymous one year ago if f(x)=-5x-13 than f^-1(x)=?

1. freckles

the first step is to solve y=-5x-13 for x.

2. 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

3. anonymous

I would add 13 to both sides and divide both sides by -5 which i guess would leave me with 5=x

4. anonymous

I don't understand how to do the same with y though

5. jim_thompson5910

|dw:1436928354040:dw|

6. jim_thompson5910

first add 13 to both sides |dw:1436928386487:dw|

7. 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

8. jim_thompson5910

after adding 13 to both sides, we now have y+13 = -5x with me so far?

9. anonymous

so far yes

10. jim_thompson5910

|dw:1436928497040:dw|

11. 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|

12. jim_thompson5910

-5 divided by itself gives 1 1 times x = x, so the '1' goes away leaving just x behind |dw:1436928578962:dw|

13. 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 $\Large f^{-1}(x) = \frac{x+13}{-5}$

14. anonymous