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

Please be sure to clearly explain your steps and support your arguments. 

I need a really good explanation please! Thank you!

Guest Nov 11, 2014

Best Answer 

 #1
avatar+93025 
+10

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

Let's find the inverse.....let  p(x) = y

y = 2x3 - 113       add 113 to both sides

y + 113  = 2x3     divide both sides by 2

( y + 113 ) / 2   = x3    take the cube root of both sides

3√[( y + 113) / 2]  = x       exchange x and y

3√[( x + 113) / 2]  = y       for "y"  write q(x)

q(x) = 3√[( x + 113) / 2]     so q(137) = 3√[( 137 + 113) / 2] = 3√125  = 5

 

CPhill  Nov 11, 2014
 #1
avatar+93025 
+10
Best Answer

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

Let's find the inverse.....let  p(x) = y

y = 2x3 - 113       add 113 to both sides

y + 113  = 2x3     divide both sides by 2

( y + 113 ) / 2   = x3    take the cube root of both sides

3√[( y + 113) / 2]  = x       exchange x and y

3√[( x + 113) / 2]  = y       for "y"  write q(x)

q(x) = 3√[( x + 113) / 2]     so q(137) = 3√[( 137 + 113) / 2] = 3√125  = 5

 

CPhill  Nov 11, 2014
 #2
avatar+94202 
0

That looks like fun Chris :)

Melody  Nov 12, 2014
 #3
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0

Wait, but doesn't ((137+133)/2)^(1/3) simplify into (270/2)^(1/3) which is (135/2)^(1/3), not (125/2)^1/3. 

Guest Aug 2, 2016

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