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# Hard question!!

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Let p(x) = 2x^3 - 113 and let q be the inverse of p. Find q(137).

Thanks for whoever is going to answer this!!!

MIRB16  Jul 22, 2017
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Let p(x) = 2x^3 - 113 and let q be the inverse of p. Find q(137)

Note that the inverse just reverses the original coordinates

So the coordinates of the inverse are ( 137, x)

So....putting 137 into the inverse sends us back to the otiginal "x"

So....the original coordinates were  ( x, 137 )

And x will equal  q (137)

So...all we need to do is to set p = 137 and solve to find this otiginal x

2x^3 - 113  = 137   add 113 to both sides

2x^3 = 250  divide both sides by 2

x^3  = 125   take the cube root of both sides

x = 5   and this is q(137)

Proof...I won't derive it but the inverse q  is   ∛ [ ( x + 113) / 2 ]

And  q (137)  =  5

CPhill  Jul 22, 2017
edited by CPhill  Jul 22, 2017
edited by CPhill  Jul 22, 2017

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