Question

if f(x)= x-1/x+1,x is not equal to 1, show that f(f(x))=-1/x,where x is not equal to 0​

Answer 1

Solution:

if f(x)= x-1/x+1,x is not equal to 1, show that f(f(x))=-1/x,where x is not equal to 0.

f(x) = (x-1)/(x+1)

LHS = f[f(x)]

= f[(x-1)/(x+1)]

= [(x-1)/(x+1)-1]/[(x-1)(x+1)+1]

= [(x-1)-(x+1)]/[(x-1)+(x+1)]

= (x-1-x-1)/(x-1+x+1)

= (-2)/(2x)

= -1/x

= RHS

Hence , prooved.

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Answer 2

Answer:

the correct answer is -1/x