Limit Continuity and Differentiability 7 Question 28

28. Let f:RR,g:RR and h:RR be differentiable functions such that f(x)=x3+3x+2,g(f(x))=x and h(g(g(x)))=x for all xR. Then,

(2016 Adv.)

(a) g(2)=115

(b) h(1)=666

(c) h(0)=16

(d) h(g(3))=36

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Answer:

Correct Answer: 28. (b)

Solution:

  1. y=ax2(xa)(xb)(xc)+bx(xb)(xc)+c(xc)+1

=ax2(xa)(xb)(xc)+bx(xb)(xc)+x(xc)

=ax2(xa)(xb)(xc)+x(xc)bxb+1=ax2(xa)(xb)(xc)+x(xc)x(xb)=x2(xc)(xb)ax1+1y=x3(xa)(xb)(xc)

logy=logx3log(xa)(xb)(xc)

logy=3logxlog(xa)log(xb)log(xc)

On differentiating, we get

yy=3x1xa1xb1xcyy=1x1xa+1x1xb+1x1xcyy=ax(xa)bx(xb)cx(xc)yy=ax(ax)+bx(bx)+cx(cx)yy=1xaax+bbx+ccx



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