Question

find the range of f(x) = x2+2x+1/x2-8x+12

Answer 1

Here , x-6 and x-2 both are ≠ 0 so x cannot be= 2 or 6 . becuz something divided by 0 is undefined. so its range is all real numbers except 0. becuz if any function is 0 then it is in undetermined form. or its range can be [ R,0)

Answer 2

Answer:

$R=(-\infty,\infty)\{y|y\in \mathbb{R}\}$

Step-by-step explanation:

Given : Expression $f(x)=\frac{x^2+2x+1}{x^2-8x+12}$

To find : The range of the function?

Solution :

First we factor the denominator,

$f(x)=\frac{x^2+2x+1}{x^2-8x+12}$

$f(x)=\frac{(x+1)^2}{x^2-6x-2x+12}$

$f(x)=\frac{(x+1)^2}{x(x-6)-2(x-6)}$

$f(x)=\frac{(x+1)^2}{(x-6)(x-2)}$

Range is defined as all possible values of y where function is defined.

Refer the attached figure below for graphical representation.

The range of the function is all real number.

$R=(-\infty,\infty)\{y|y\in \mathbb{R}\}$