Question

f(x) = |2x - 4|, find f( x ) = -16

Explanation:

Step1: Analyze absolute value property

The absolute value of any real number, denoted as $|A|$, is always non-negative, meaning $|A| \geq 0$ for all real $A$.

Step2: Compare with given equation

We are asked to solve $|2x - 4| = -16$. Since the left-hand side is an absolute value (always $\geq 0$) and the right-hand side is a negative number ($-16 < 0$), there is no real number $x$ that can satisfy this equation.

Answer:

There is no real solution for $x$ (no real value of $x$ makes $f(x) = -16$).