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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 given problem step by step.

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

Step 1: Opposite of [tex]\( g(x) \)[/tex]

To find the opposite of [tex]\( g(x) \)[/tex], we simply negate the function:
[tex]\[ -g(x) = -(x - 6) \][/tex]
Distributing the negative sign, we get:
[tex]\[ -g(x) = -x + 6 \][/tex]

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

Step 2: Sum of [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]\[ g(x) + (-g(x)) \][/tex]
Substituting the given expressions, we have:
[tex]\[ g(x) = x - 6 \][/tex]
[tex]\[ -g(x) = -x + 6 \][/tex]

Now, adding these two together:
[tex]\[ g(x) + (-g(x)) = (x - 6) + (-x + 6) \][/tex]

Combining like terms:
[tex]\[ g(x) + (-g(x)) = (x + (-x)) + (-6 + 6) \][/tex]
[tex]\[ g(x) + (-g(x)) = 0 + 0 \][/tex]
[tex]\[ g(x) + (-g(x)) = 0 \][/tex]

So, to summarize:

1. [tex]\( -g(x) = -x + 6 \)[/tex]
2. [tex]\( g(x) + (-g(x)) = 0 \)[/tex]

Thus, the final solution is:

[tex]\[ -g(x) = -x + 6 \][/tex]
[tex]\[ g(x) + (-g(x)) = 0 \][/tex]
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