Let f(x) = (x+3)/(x+1)
(a) Find the domain and range of f(x)
(b) Show that f(x) is one-to-one function and find the inverse function f-1(x)
My attempt for (a) : since the function is undefined when x = -1 thus the domain is IR\{-1}
But my problem is how i can find the range of the function. is the range of the function is IR except the value when x=-1. BUT how i can find the value of the function at x=-2???
If I were to find the range of the function by graph, how f(x) graph looks like???
next if i want to show that f(x) is one-to-one function then i have to find the inverse of it... is there any other way to show that it is one-to-one???
the way i find the inverse :
let f(x) = y
thus have to find x in terms of y
y = x+3/x+1
but how can i group the x so that i can found x in terms of y??? since they are separated by quotient....