Question

f(x) =x+5/x-10
what is the inverse of f(x) and how do I determine the range of the inverse

Answer 1

put y=x+5/(x-10)
y=(x^2-10x+5)/(x-10)
x^2-10x+5=xy-10y
x^2-(10+y)x+(5+10y)=0
from here find the roots of x using quadratic formula
and f^-1(y)=x
so the function of y u get is the inverse function

Answer 2

Range of inverse is same as domain of original function
domain is all real numbers, except x not equal to 10