Question

if f:(1,∞)–(2,∞) is given by f(x)= x+(1/x) then find f inverse

Answer 1

Inverse means product gives answer 1.
for eg .if f(x)=x,
inverse is find out by substituting (1÷x)for x.
f^-1(1÷x)=(1÷x)

so f× f^-1 (x)= x×(1÷x)=1...

Like here also , substituting x by (1÷x)...

here when substituting,
f^-1(x)=x+(1÷x) remain same as f(x).

the change will be written in the defining points.
so domain and range of f(x) becomes range and domain of f^-1(x) respectively.

so here inverse is
f^-1(x)=x+(1÷x) itself
but defined from
(2,infinity) -> (1,infinity)...

Like if satisfied