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what is the inverse of the function f(x)=2/3x^3-1

the options are 

g(x)=^3√6x-6 /2

g(x)=^3√12x+12/2

g(x)=^3√6x+6 /2

g(x)=^3√12x-12/2

THANKS

 Jan 23, 2021
 #1
avatar+116126 
+1

f(x)  =(2/3)x^3  -1

 

y= (2/3)x^3   - 1

 

get x by itself...."swap"  x and y

 

add 1 to both sides

 

y + 1  = (2/3)x^3     mutiply both sides by    3/2

 

(3/2)y +3/2   = x^3           take the  cbe root of both sides

 

∛ [ (3y + 3)  / 2  ]   =  x

 

Inside the radical, nutiply numerator, denominator  by 4

 

∛ [ (12y + 12)  / 8  ]   = x

 

∛ (12y + 12)  / 2      =  x      "sap  x and y

 

∛ (12x + 12)   / 2   =  y   =   the nverse 

 

 

cool cool cool

 Jan 23, 2021

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