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

1 Answer
Mar 25, 2016

Answer:

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