If f is a real function defined by `f(x)=(x-1)/(x+1)`, then prove that – InterviewSolution

InterviewSolution

1.	If f is a real function defined by `f(x)=(x-1)/(x+1)`, then prove that `f(2x)=(3f(x)+1)/(f(x)+3)`
Answer» We have, `f(x)=(x-1)/(x+1)`. `:.(3f(x)+1)/(f(x)+3)=(3((x-1)/(x+1))+1)/(((x-1))/((x+1))+3)` `=((3x-3)+(x+1))/((x+1))xx((x+1))/((x-1)+(3x+3))=(2x-1)/(2x+1)=f(2x)`. Hence, `f(2x)=(3f(x)+1)/(f(x)+3)`.

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