Certainlyy = f(x)is strictly increasing in[1,+infty)and

lim_ {x to +infty} f(x) = +infty

This means that

f : [1,+infty) -> [1,+infty)

is bijective, as a consequence there existsf^{ -1 }.

Takelogin both sides ofy = f(x), solve the quadratic equation on x and choose the positive branch.