How do you find the inverse of #f(x) = 6x^3 - 3#?

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Answer 1 · 2015-09-10T21:47:27

#f^(-1)(x)=root(3)((x+3)/6)#

Step 1: Replace #f(x)# with #y#.

#y=6x^3-3#

Step 2: Solve for #x#.

By adding 3 to both sides,

#y+3=6x^3#

By dividing both sides by 6,

#(y+3)/6=x^3#

By taking the cube-root of both sides,

#root(3)((y+3)/6)=x#

Step 3: Swap #x# and #y#.

#root(3)((x+3)/6)=y#

Step 4: Replace #y# by #f^(-1)(x)#.

#f^(-1)(x)=root(3)((x+3)/6)#