## anonymous 5 years ago How do you get this?:) let f(x)=(x+2)/(x+8) f^-1(-9)=?

1. amistre64

you want the inverse of f(x)

2. anonymous

$f^(-1)(x) = -(2 (4 x-1))/(x-1)$

3. amistre64

the inverse is gotten suslly by switching x and y and resolves for y

4. anonymous

You don't have to find the inverse, Just plug f(x)=-9, and then solve for x. That value of x is the inverse at x=-9.

5. anonymous

let y = x+2 / x+8 yx + 8y = x+2 x(1-y) = 8y-2 x = (8y-2)/1-y which gives u d inverse now switch x and y and put in d value of x to get y

6. anonymous

thank you!:)

7. amistre64

x=(y+2)/(y+8) x(y+8)=y+2 xy +8x = y+2 xy - y = -8x +2 y(x-1) = -8x+2 y = (-8x+2) ------- (x-1)

8. amistre64

y = (-8(-9)+2)/(-9-1) y = 74/-10 = -7.4

9. anonymous

welll i did the very same

10. amistre64

yay!! its verified then ;)

11. anonymous

A simpler method, is to plug f(x)=-9 and then solve for x: $-9={x+2 \over x+8} \implies -9x-72=x+2 \implies 10x=-74 \implies x=- 7.4$ So,$f^{-1}(-9)=-7.4$

12. anonymous

I like my method :P

13. amistre64

your method is just the same method rehashed lol

14. anonymous

Haha, not really.

15. anonymous

admit it, mine is better :P