1. anonymous

can you solve $-5x-11=7$?

2. anonymous

for example i mean it takes two steps only

3. anonymous

$x=-\frac{ -18 }{ ?5}$

4. anonymous

well $\frac{18}{5}$yes how did you do it?

5. anonymous

I did the work and checked it with a calculator

6. anonymous

"the work" being what ?

7. anonymous

but is that all there is to it?

8. anonymous

two steps right? what were those two steps?

9. anonymous

switch x and y, solve for y and x, and substitute f^-1 for y

10. anonymous

my school teaches it in three steps

11. anonymous

but that isn't the answer they want

12. anonymous

ok all i was trying to point out is that if you can solve $-5x-11=7$ that means if you know the output 7, you know the input $$\frac{18}{5}$$ the two steps where a) add 11 b) divide by $$-5$$ that is what the inverse does

13. anonymous

if you cannot do it in your head (which you can) solve $-5y-11=x$ for $$y$$ same two steps a) add 11$-5y=x+11$divide by $$-5$$ $y=\frac{x+11}{-5}$

14. anonymous

or if you want to pull out the minus sign, write $f^{-1}(x)=-\frac{x+11}{5}$