Question

Given f(x)=log11x, find f–1(x) and f–1(2).

Answer 1

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

Answer 2

Can anyone help?

Answer 3

u can use ~ for space

Answer 4

An inverse of logarithmic is going to be an exponential.

Answer 5

Inverse?

Answer 6

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

Answer 7

Oh okay.. I suck at these to be honest

Answer 8

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.

Answer 9

\[x=\log_{11} y\]

Answer 10

like that?

Answer 11

for the third step, you will need to know that

\(\Large\color{black}{ \displaystyle \color{red}{\rm a}=\log_{\color{green}{\rm b}}(\color{blue}{\rm c}) ~~~~\Longrightarrow~~~~\color{green}{\rm b}^\color{red}{\rm a}=\color{blue }{\rm c} }\).

Answer 12

yes, for the first two steps, that is correct

Answer 13

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

Answer 14

\[11^{x}\]

Answer 15

=y

Answer 16

\[11^{x}=y\]

Like that? @SolomonZelman

Answer 17

yes

Answer 18

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

Answer 19

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

Answer 20

where did you get the 2 from?

Answer 21

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

Answer 22

ohhh okay I got it now

Answer 23

Can you help me with another one? @SolomonZelman

Answer 24

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

Answer 25

will see.

Answer 26

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