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## anonymous 4 years ago let f(x)= 1/x+9 what is f^-1(x)=?

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1. nenadmatematika

x+9

2. Mertsj

$x=\frac{1}{y+9}$

3. Mertsj

$x(y+9)=1$

4. nenadmatematika

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

5. Mertsj

$y+9=\frac{1}{x}$

6. Mertsj

$y=\frac{1}{x}-9$

7. Mertsj

$y=\frac{1-9x}{x}$

8. anonymous

thanks guys!

9. cristiann

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.

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