If #g(x)= 1+(x)^(1/3)# and #f(g(x))=3-(x)^(1/3)+x#, then find #f(x)#?

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Answer 1 · 2018-06-03T04:25:15

Given

#g(x)= 1+(x)^(1/3)# and #f(g(x))=3-(x)^(1/3)+x#

So

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

Now let #1+(x)^(1/3)=z#

#=>x=(z-1)^3#

Hence

#f(z)=3-((z-1)^3)^(1/3)+(z-1)^3#

#=>f(z)=3-z+1+z^3-3z^2+3z-1#

#=>f(z)=z^3-3z^2+2z+3#

Replacing z by x we get

#=>f(x)=x^3-3x^2+2x+3#