If #f(x)=2x^3 -1.# Hence how do you find #f^ -1(x)#?

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Answer 1 · 2018-05-20T06:25:19

The inverse is #=root(3)((x+1)/2)#

#f(x)=2x^3-1#

Let

#y=2x^3-1#

Then,

#2x^3=y+1#

#x^3=(y+1)/2#

#x=root(3)((y+1)/2)#

Therefore,

#f^-1(x)=root(3)((x+1)/2)#

Verification :

#f(f^-1)(x)=f(root(3)((x+1)/2))=2*(root(3)((x+1)/2))^3-1#

#=(x+1-1)=x#

graph{(y-2x^3+1)(y-root(3)((x+1)/2))(y-x)=0 [-10, 10, -5, 5]}