# Question #4ab13

May 30, 2017

$f \left(a\right)$ means that you substitute "a" for every x within $f \left(x\right)$ and then do the calculations.

#### Explanation:

$f \left(5\right)$ means you substitute 5 for x everywhere you see x in the given function, f(x):

$f \left(5\right) = - 8 | - 10 + 5 | \leftarrow$ we substituted 5 for x.

Now, we just do the calculations.

$f \left(5\right) = - 8 | - 5 | \leftarrow$ this is $- 10 + 5 = - 5$

$f \left(5\right) = - 8 \left(5\right) \leftarrow$ this is $| - 5 | = 5$

$f \left(5\right) = - 40 \leftarrow$ answer

May 30, 2017

$- 40$

#### Explanation:

So, the question is, if $f \left(x\right)$ equals $- 8 \left\mid - 10 + x \right\mid$, what does $f \left(5\right)$ equal.

Well, let's start by replacing $x$ with $5$, because now the equation asks for the function of $5$:

$- 8 \left\mid - 10 + 5 \right\mid$

Let's simplify the values within the grouping system ($\left\mid \textcolor{w h i t e}{000} \right\mid$)

$- 8 \left\mid - 5 \right\mid$

Because absolute value is a measure of distance, it can never represent a negative number. There's no such thing as $- 5$ feet. Even if a person moves backward $10$ meters, they have moved $10$ meters, but it is not negative.

What that means is, an absolute value of a negative number is a positive number. So, $\left\mid - 5 \right\mid$ is $5$:

$- 8 \left(5\right)$

$- 40$