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anonymous
 one year ago
Let f(x)=10x10. Find the value of (f o f^1)(10)
anonymous
 one year ago
Let f(x)=10x10. Find the value of (f o f^1)(10)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0f(x) is a onetoone function (it's a line) so (f o f^1)(10) = 10

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0basically, inverses "undo" each other, so you end up with the same value

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh ok and so i plug the 10 into the original equation or would that be the answer?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0Nope.\[f(f^{1}(10)) = x\]\[10=x\] That's basically what is going on. \[f(10)=10x10 = 110 \ne 10 \]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0Sorry, forgot to substitute by 10 in for x. \(f(10)=10(10)10 = 110\)*

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.3\[f(x) = 10x10\\[3ex] x=10\Big(f^{1}(x)\Big)10\\ x+10 = 10(f^{1}(x))\\ f^{1}(x)=\frac {x+10}{10}\\[3ex]f\circ f^{1}(x)=f\Big(\frac {x+10}{10}\Big)\\ \qquad\qquad\quad = 10\Big(\frac {x+10}{10}\Big)10\\ \qquad\qquad\quad = x+1010\\ \qquad\qquad\quad =x\\[2ex] f\circ f^{1}(10) =10\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[f \circ f^{1}(x)=x\] A function and it's inverse cancel each other out, leaving you with the independent variable x

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0I like the way @UnkleRhaukus proved it and then found the value.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0mmhm, it has a beauty of it's own
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