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anonymous
 one year ago
if h(x)=2x/2, find (h o h^1)(2)
A)X
B)1/2
C)2
D)0
THANK YOU SO MUCH!!
anonymous
 one year ago
if h(x)=2x/2, find (h o h^1)(2) A)X B)1/2 C)2 D)0 THANK YOU SO MUCH!!

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jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1is the function this? \[\Large h(x) = 2  \frac{x}{2}\] OR is the function this? \[\Large h(x) = \frac{2x}{2}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1442458455816:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1ok so the first one I wrote

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So yes, the first one you stated. Thank you.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1think of it as \[\Large y = 2  \frac{x}{2}\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1then swap x and y \[\Large x = 2  \frac{y}{2}\] then solve for y

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what about the h o h ^1(2)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1I would first multiply both sides by 2 that clears out the fraction

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so you'll have 2x = 4  y isolate y

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then what happens with the h o h ^1 (2). That is my primary concern.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1y=2x4 will turn into y = 2x+4

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so the inverse is \[\Large h^{1}(x) = 2x+4\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large (h \circ h)^{1}(2)\] is the same as \[\Large h(h^{1}(2))\] the first task is to compute \(\Large h^{1}(2)\)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1sorry I meant to say \(\Large (h \circ h^{1})(2)\)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1anyways, what output do you get when you plug x = 2 into the inverse

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1then that 0 is plugged into the h(x) function

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large \Large h(\color{red}{h^{1}(2)}) = h(\color{red}{0})\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you so much for the walkthrough, it really helped me. :)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so you found what h(0) is?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1plug it into 2  (x/2)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yeah that part is 0, but we're not done yet

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh, so it is just 2?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you take that result and plug it into h(x)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1ultimately, the final result is 2 you'll find that \[\Large (h \circ h^{1})(x) = x\] for any x value

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1because the inverse essentially "undoes" what the original function does
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