Question

let f(x)= 1/x+9

what is f^-1(x)=?

Answer 1

x+9

Answer 2

\[x=\frac{1}{y+9}\]

Answer 3

\[x(y+9)=1\]

Answer 4

oh you're true Mertsj...it's the inverse function :D

Answer 5

\[y+9=\frac{1}{x}\]

Answer 6

\[y=\frac{1}{x}-9\]

Answer 7

\[y=\frac{1-9x}{x}\]

Answer 8

thanks guys!

Answer 9

This question is either tricky or just plain sloppy ...
First: it's not clear the form of the function
\[f_{1}(x)=\frac{1}x+9\]
or
\[f_{2}(x)=\frac{1}{x+9}\]
Then:
no matter which function, you still have problems, because of the domain and codomain of the functions:
For f1:
\[x \neq 0, y \neq 9\]
so only if the function is in the form
\[f_{1}:\mathbb{R}^{*}\rightarrow \mathbb{R} \setminus (9) \]
it is bijective (one-to-one/injective and onto/surjective)

For the second function, you have the same type of problem, with
\[x \neq -9, y \neq 0\]
Only now you may talk about the expression of the inverse.