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Adi3
 one year ago
Will medal
Please help.
g(x) = (x)/x5
(i) find g^1(x)
(ii) find g(6) and g^1(1)
Adi3
 one year ago
Will medal Please help. g(x) = (x)/x5 (i) find g^1(x) (ii) find g(6) and g^1(1)

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butterflydreamer
 one year ago
Best ResponseYou've already chosen the best response.1oh gosh xD I always get confused when i do inverse functions. Firstly, let's start off with our function: \[g(x) = \frac{ x }{ x  5 }\] Rename g(x) as "y" \[y = \frac{ x }{ x  5}\] Multiply both sides by (x  5) \[y (x  5) = x\] Expand . \[xy  5y = x\] move all the x's to one side. \[xy  x = 5y\] Factorise out the "x". \[x ( y  1) = 5y\] Make "x" the subject. \[x = \frac{ 5y }{ y  1}\] Now to find the inverse, simply swap the x's with y's and vice versa :) Then rename the function as it's inverse \[g ^{1} (x)\]

Adi3
 one year ago
Best ResponseYou've already chosen the best response.0so i get \[\left(\begin{matrix}5x \\ x1\end{matrix}\right)\]

butterflydreamer
 one year ago
Best ResponseYou've already chosen the best response.1er.. if that's a fraction then yes LOL. \[g^{1} (x) = \frac{ 5x }{ x1 } \]

Adi3
 one year ago
Best ResponseYou've already chosen the best response.0yes, what about the (ii) one

butterflydreamer
 one year ago
Best ResponseYou've already chosen the best response.1For part (II). We know that \[g(x) = \frac{ x }{ x  5 }\] so to find g(6) sub x = 6 and we get: \[g(6) = \frac{ 6 }{ 6  5 } = ?\] Do the same for g^1(x) but sub x = 1 \[g^{1} (x) = \frac{ 5x }{ x1} \rightarrow g^{1} (1) = \frac{ 5(1) }{ 1  1 } = ?\]

butterflydreamer
 one year ago
Best ResponseYou've already chosen the best response.1?? take a look at what i typed in my prev. post :) i showed you both g(6) and g^1 (1)
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