Question

f(x) =x/x-1

then f^-1(x) = ?
​

Answer 1

Answer:

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

Let y=1/x

then,by definition, f(y)=y/(y-1)

or f(y)=(1/x)/((1/x)-1)

or f(y)=(1/x)/((1-x)/x)

or f(y)=1/(1-x)

or f(1/x)=1/(1-x) ……. (In terms of x)

Now,f(y)+f(x)=x/(x-1)+1/(1-x)

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

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

or f(y)+f(x)=1

or f(1/x)=1-f(x) …….. (In terms of f(x))

l hope it will help u ☺️

Answer 2

Answer:

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

Let y=1/x

then,by definition, f(y)=y/(y-1)

or f(y)=(1/x)/((1/x)-1)

or f(y)=(1/x)/((1-x)/x)

or f(y)=1/(1-x)

or f(1/x)=1/(1-x) ……. (In terms of x)

Now,f(y)+f(x)=x/(x-1)+1/(1-x)

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

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

or f(y)+f(x)=1

or f(1/x)=1-f(x) …….. (In terms of f(x))