Let f ( x )= x +1 x -1 for all x 1 . Let f ¹( x )= f ( x ), f ²( x )= f ( f ( x )) and generally f^ n (x)=f (f^ n-1 (x) ) for n1 Let P = f ¹(2) f ²(3) f ³(4) f ⁴(5) Which of the following is a multiple of P -

Question

Let f ( x )= x +1 x -1 for all x 1 . Let f ¹( x )= f ( x ), f ²( x )= f ( f ( x )) and generally f^ n (x)=f (f^ n-1 (x) ) for n>1 Let P = f ¹(2) f ²(3) f ³(4) f ⁴(5) Which of the following is a multiple of P -

Quantrex Academy · Accepted Answer

Correct answer: B. 375

array l f(x)= x+1 x-1 f²(x)=f(f(x))=f ( x+1 x-1 )= x+1 x-1 +1 x+1 x-1 -1 =x f³(x)=f(x)= x+1 x-1 f⁴(x)=x P=f(2) f³(3) f³(4) f⁴(5) P=3 3 5 3 5=75 array Multiple of P is 375

Let f ( x )= x +1 x -1 for all x 1 . Let f ¹( x )= f ( x ), f ²( x )= f ( f ( x )) and generally f^ n (x)=f (f^ n-1 (x) ) for n>1 Let P = f ¹(2) f ²(3) f ³(4) f ⁴(5) Which of the following is a multiple of P -

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