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If `a_0 = x,a_(n+1)= f(a_n)`, where `n = 0, 1, 2, ...,` then answer thefollowing questions. If `f (x) = msqrt(a-x^m),x lt0,m leq 2,m in N`,thenA. `a_(n)=x, n=2k+1,` where k is an integerB. `a_(n)=f(x) " if " n=2k,` where k is an integerC. The inverse of `a_(n)` exists for any value of n and mD. None of these |
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Answer» Correct Answer - D Given `a_(n+1)=f(a_(n))` Now, `a_(1)=f(a_(0))=f(x)` `or a_(2)=f(a_(1))=f(f(a_(0)))=fof(x)` `or a_(n)=(fofofof …f(x))/("n times")` `a_(1)=f(x)=(a-x^(m))^(1//m)` `or a_(2)=f(f(x))=[a-{(a-x^(m))^(1//m)}^(m)]^(1//m)=x` `or a_(3)=f(f(f(x)))=f(x)` Obviously, the inverse does not exist when m is even and n is odd. |
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