Question

What is the domain and range of `y = y = (x^2 - 1) / (x+1)`?

Answer 1

a) `y=(x^2-1)/(x+1)= (x-1)(x+1)/(x+1)=x-1`
b) Domain: `ℝ = {x | -∞ < x <∞}` All Real x are possible
c) Range: `ℝ = {f(x)=y | -∞ < f(x) <∞}` All Real y are possible

Explanation:

Given: `y=(x^2-1)/(x+1)`
Required the Domain and range:
Solution Strategy:
a) Simplify the function, `y=f(x)`
b) Domain: identify all possible value of `x`
c) Range: Identify all possible results of the function, `f(x)`

a) `y=(x^2-1)/(x+1)= (x-1)(x+1)/(x+1)=x-1`
b) Domain: `ℝ = {x | -∞ < x <∞}` All Real x are possible
c) Range: `ℝ = {f(x)=y | -∞ < f(x) <∞}` All Real y are possible