Answered

IDNLearn.com: Where your questions meet expert answers and community support. Discover detailed and accurate answers to your questions from our knowledgeable and dedicated community members.

Given:
[tex]\[ g(x) = x - 6 \][/tex]

If the opposite of [tex]\( g(x) \)[/tex] is [tex]\( -g(x) \)[/tex], then:
[tex]\[ -g(x) = \square \][/tex]

[tex]\[ g(x) + (-g(x)) = \square \][/tex]

Sagot :

GinnyAnsweridn
Let's solve the question step-by-step.

First, we are given the function [tex]\( g(x) = x - 6 \)[/tex].

### Step 1: Finding [tex]\(-g(x)\)[/tex]
The opposite of [tex]\( g(x) \)[/tex] is [tex]\(-g(x)\)[/tex]. To find [tex]\(-g(x)\)[/tex], we multiply [tex]\( g(x) \)[/tex] by [tex]\(-1\)[/tex]:

[tex]\[ -g(x) = -1 \cdot (x - 6) \][/tex]

Distribute the [tex]\(-1\)[/tex] across the terms inside the parentheses:

[tex]\[ -g(x) = -x + 6 \][/tex]

So, we have:

[tex]\[ -g(x) = 6 - x \][/tex]

### Step 2: Adding [tex]\( g(x) \)[/tex] and [tex]\(-g(x)\)[/tex]
Next, we need to find the sum of [tex]\( g(x) \)[/tex] and [tex]\(-g(x) \)[/tex]:

[tex]\[ g(x) + (-g(x)) = (x - 6) + (6 - x) \][/tex]

Combine the terms:

[tex]\[ (x - 6 + 6 - x) \][/tex]

Notice that [tex]\( x \)[/tex] and [tex]\(-x\)[/tex] cancel each other out:

[tex]\[ x - x + 6 - 6 = 0 \][/tex]

So, the sum is:

[tex]\[ g(x) + (-g(x)) = 0 \][/tex]

### Final Answer
[tex]\[ -g(x) = 6 - x \][/tex]
[tex]\[ g(x) + (-g(x)) = 0 \][/tex]
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com is your source for precise answers. Thank you for visiting, and we look forward to helping you again soon.