MathematicsIf f(x)=x3+3x+4 and g is the inverse of f, then the value of 9|ddx(g(x)g(g(x)))| at x=4 is equal to

If f(x)=x3+3x+4 and g is the inverse of f, then the value of 9|ddx(g(x)g(g(x)))| at x=4 is equal to

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    Solution:

    f(g(x))=xf(g(x))g(x)=1

    ddx(g(x)g(g(x)))=g(g(x))g(x)g(g(x))g(x)g(x)(g(g(x)))2

    Also, g(4)=0 and g(4)=1f(0)

    f(x)=3x2+3f(0)=3,g(g(4))=g(0)=1

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