Question

1. $f(x)=\frac{x^2 + 2x + 1}{2 - x}$; $f(-7), f(-2)$

express your answer in set builder notation.

Explanation:

Step1: Substitute $x=-7$ into $f(x)$

$f(-7)=\frac{(-7)^2 + 2(-7) + 1}{2 - (-7)}$

Step2: Simplify numerator and denominator

Numerator: $(-7)^2 + 2(-7) + 1 = 49 - 14 + 1 = 36$
Denominator: $2 - (-7) = 2 + 7 = 9$
$f(-7)=\frac{36}{9}=4$

Step3: Substitute $x=-2$ into $f(x)$

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

Step4: Simplify numerator and denominator

Numerator: $(-2)^2 + 2(-2) + 1 = 4 - 4 + 1 = 1$
Denominator: $2 - (-2) = 2 + 2 = 4$
$f(-2)=\frac{1}{4}$

Answer:

$f(-7)=4$, $f(-2)=\frac{1}{4}$