## anonymous one year ago Given f(x)=log11x, find f–1(x) and f–1(2).

1. anonymous

$given f(x)=\log_{11} x, find f ^{-1}(x) and f ^{-1}(2)$

2. anonymous

Can anyone help?

3. SolomonZelman

u can use ~ for space

4. SolomonZelman

An inverse of logarithmic is going to be an exponential.

5. anonymous

Inverse?

6. SolomonZelman

$${\rm f}^{-1}(x)$$ is a notation for an inverse function.

7. anonymous

Oh okay.. I suck at these to be honest

8. SolomonZelman

Your function is: $$\large\color{black}{ \displaystyle f(x)=\log_{11}(x) }$$ 1) replace f(x) with y. 2) switch x and y (write y instead of x, and write y instead of x) 3) {solve for/ isolate the} y.

9. anonymous

$x=\log_{11} y$

10. anonymous

like that?

11. SolomonZelman

for the third step, you will need to know that $$\Large\color{black}{ \displaystyle \color{red}{\rm a}=\log_{\color{green}{\rm b}}(\color{blue}{\rm c}) ~~~~\Longrightarrow~~~~\color{green}{\rm b}^\color{red}{\rm a}=\color{blue }{\rm c} }$$.

12. SolomonZelman

yes, for the first two steps, that is correct

13. SolomonZelman

now, apply the third step to that (to $$x=\log_{11}y$$ )

14. anonymous

$11^{x}$

15. anonymous

=y

16. anonymous

$11^{x}=y$ Like that? @SolomonZelman

17. SolomonZelman

yes

18. SolomonZelman

then replcae y by $$f^{-1}(x)$$

19. SolomonZelman

|dw:1435782711063:dw|

20. SolomonZelman

then for f$$^{-1}$$(2) plug in 2 for x, into the last expression that I drew

21. anonymous

where did you get the 2 from?

22. SolomonZelman

you need $$f^{-1}(2)$$. that is your second part.

23. anonymous

ohhh okay I got it now

24. anonymous

Can you help me with another one? @SolomonZelman

25. SolomonZelman

ok, but I am helping another person right now... well I am attempting to help that person.

26. SolomonZelman

will see.

27. anonymous

Okay.. I'll just open a new question.