For `x in R-{0,1}, " let " f_(1)(x)=(1)/(x), f_(2)(x)=1-x and f_(3)(x)=(1)/(1-x)` be three given functions. If a function, J(x) satisfies `(f_(2) @[email protected]_(1))(x)=f_(3)(x), " then " J(x)` is equal toA. `f_(2)(x)`B. `f_(3)(x)`C. `f_(1)(x)`D. `(1)/(x)f_(3)(x)`

For `x in R-{0,1}, " let " f_(1)(x)=(1)/(x), f_(2)(x)=1-x and f_(3)(x)

1.	For `x in R-{0,1}, " let " f_(1)(x)=(1)/(x), f_(2)(x)=1-x and f_(3)(x)=(1)/(1-x)` be three given functions. If a function, J(x) satisfies `(f_(2) @[email protected]_(1))(x)=f_(3)(x), " then " J(x)` is equal toA. `f_(2)(x)`B. `f_(3)(x)`C. `f_(1)(x)`D. `(1)/(x)f_(3)(x)`
Answer» Correct Answer - B We have, `f_(1)(x)=(1)/(x), f_(2)(x)=1-x and f_(3)(x)=(1)/(1-x)` Also, we have `(f_(2)@ J @f_(1))(x)=f_(3)(x)` `rArr f_(2)(([email protected]_(1)(x))=f_(3)(x)` `rArr f_(2)(J(f_(1)(x))=f_(3)(x)` `rArr 1-J(f_(1)(x))=(1)/(1-x)` ` " "[ because f_(2)(x)=1-x and f_(3)(x)=(1)/(1-x)]` `rArr 1-J((1)/(x))=(1)/(1-x) " [ because f_(1)(x)=(1)/(x)]` `rArr J((1)/(x))=1-(1)/(1-x)` `=(1-x-1)/(1-x)= (-x)/(1-x)` Now, put `(1)/(x)=X,` then `J(X)=((1)/(X))/(1-(1)/(X)) " "[ because x=(1)/(X)]` `=(-1)/(X-1)=(1)/(1-X)` ` rArr J(X)=f_(3)(X) or J(x)=f_(3)(x)`