## anonymous one year ago Let f(x)=10x-10. Find the value of (f o f^-1)(-10)

1. anonymous

f(x) is a one-to-one function (it's a line) so (f o f^-1)(-10) = -10

2. anonymous

basically, inverses "undo" each other, so you end up with the same value

3. anonymous

oh ok and so i plug the -10 into the original equation or would that be the answer?

4. Jhannybean

Nope.$f(f^{-1}(-10)) = x$$-10=x$ That's basically what is going on. $f(-10)=-10x-10 = -110 \ne -10$

5. Jhannybean

Sorry, forgot to substitute by -10 in for x. $$f(-10)=-10(-10)-10 = -110$$*

6. UnkleRhaukus

$f(x) = 10x-10\\[3ex] x=10\Big(f^{-1}(x)\Big)-10\\ x+10 = 10(f^{-1}(x))\\ f^{-1}(x)=\frac {x+10}{10}\\[3ex]f\circ f^{-1}(x)=f\Big(\frac {x+10}{10}\Big)\\ \qquad\qquad\quad = 10\Big(\frac {x+10}{10}\Big)-10\\ \qquad\qquad\quad = x+10-10\\ \qquad\qquad\quad =x\\[2ex] f\circ f^{-1}(-10) =-10$

7. anonymous

$f \circ f^{-1}(x)=x$ A function and it's inverse cancel each other out, leaving you with the independent variable x

8. Jhannybean

I like the way @UnkleRhaukus proved it and then found the value.

9. anonymous

mmhm, it has a beauty of it's own

10. anonymous

yes it does

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