Question

the graphs of two functions, f(x) and g(x), are given.
$f(x) = -|x + 6| - 5$
$g(x) = -6$
find the solution(s) to $f(x) = g(x)$.

Explanation:

Step1: Set up the equation

Set \( f(x) = g(x) \), so \( -|x + 6| - 5 = -6 \).

Step2: Solve for the absolute value

Add 5 to both sides: \( -|x + 6| = -6 + 5 = -1 \).
Multiply both sides by -1: \( |x + 6| = 1 \).

Step3: Solve the absolute value equation

The absolute value equation \( |x + 6| = 1 \) gives two cases:
Case 1: \( x + 6 = 1 \), then \( x = 1 - 6 = -5 \).
Case 2: \( x + 6 = -1 \), then \( x = -1 - 6 = -7 \).

Answer:

The solutions are \( x = -7 \) and \( x = -5 \).