Let f(x)=10x-10. Find the value of (f o f^-1)(-10)

Question

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

jhannybean · Answer

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

jhannybean · Answer

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

unklerhaukus · Answer

$$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$$

anonymous · Answer

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

jhannybean · Answer

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

anonymous · Answer

mmhm, it has a beauty of it's own

anonymous · Answer

yes it does