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Math  /  Algebra

QuestionConsider the following functions.
f(x)=xf(x) = x and g(x)=x2−14g(x) = x^2 - 14
Step 2 of 4: Find (f−g)(−2)(f - g)(-2).
Answer How to enter your answer (opens in new window)
(f−g)(−2)=(f - g)(-2) =

Studdy Solution

STEP 1

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

STEP 2

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

STEP 3

We are given two functions: f(x)=xf(x) = x and g(x)=x2−14g(x) = x^2 - 14.
Let's keep these in mind as we move forward!

STEP 4

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

STEP 5

Now, let's **substitute** x=−2x = -2 into g(x)=x2−14g(x) = x^2 - 14.

STEP 6

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

STEP 7

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

STEP 8

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

STEP 9

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

STEP 10

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

STEP 12

(f−g)(−2)=8(f - g)(-2) = 8

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