Math Snap

STEP 1

What is this asking?
We're given two functions, $f(x)$ and $g(x)$, and we need to find the difference between these functions when $x$ is $-2$.
Watch out!
Make sure to correctly substitute $-2$ into both functions and be careful with the signs when subtracting $g(x)$ from $f(x)$.

STEP 2

1. Define the functions
2. Calculate $f(-2)$
3. Calculate $g(-2)$
4. Calculate $(f - g)(-2)$

STEP 3

We are given two functions: $f(x) = x$ and $g(x) = x^2 - 14$.
Let's keep these in mind as we move forward!

STEP 4

We substitute $x = -2$ into $f(x)$.
So, $f(-2) = -2$.
Easy peasy!

STEP 5

Now, let's substitute $x = -2$ into $g(x) = x^2 - 14$.

STEP 6

This gives us $g(-2) = (-2)^2 - 14$.
Remember, squaring a negative number makes it positive!

STEP 7

So, $g(-2) = 4 - 14 = -10$.
Awesome!

STEP 8

We want to find $(f - g)(-2)$, which means $f(-2) - g(-2)$.
We've already calculated both of these values.

STEP 9

We found that $f(-2) = -2$ and $g(-2) = -10$.

STEP 10

So, $(f - g)(-2) = f(-2) - g(-2) = -2 - (-10)$.
Subtracting a negative number is the same as adding its positive counterpart.

STEP 11

Therefore, $(f - g)(-2) = -2 + 10 = 8$.
We did it!

$(f - g)(-2) = 8$