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Given the functions:

[tex]\[ f(x) = 6x \quad g(x) = |x + 5| \quad h(x) = \frac{1}{x + 7} \][/tex]

Evaluate the function [tex]\((g - h)(-8)\)[/tex] for the given value of [tex]\(x\)[/tex]. Write your answer as an integer or simplified fraction.

[tex]\((g - h)(-8)\)[/tex] is [tex]\(\square\)[/tex].



Answer :

GinnyAnswer
Sure, let's break down the problem step-by-step and evaluate the given functions for [tex]\( x = -8 \)[/tex]:

1. Evaluate [tex]\( g(x) \)[/tex] at [tex]\( x = -8 \)[/tex]:

The function [tex]\( g(x) \)[/tex] is given by:
[tex]\[ g(x) = |x + 5| \][/tex]

Substitute [tex]\( x = -8 \)[/tex] into the function:
[tex]\[ g(-8) = |-8 + 5| = |-3| = 3 \][/tex]

So, [tex]\( g(-8) = 3 \)[/tex].

2. Evaluate [tex]\( h(x) \)[/tex] at [tex]\( x = -8 \)[/tex]:

The function [tex]\( h(x) \)[/tex] is given by:
[tex]\[ h(x) = \frac{1}{x + 7} \][/tex]

Substitute [tex]\( x = -8 \)[/tex] into the function:
[tex]\[ h(-8) = \frac{1}{-8 + 7} = \frac{1}{-1} = -1 \][/tex]

So, [tex]\( h(-8) = -1 \)[/tex].

3. Evaluate [tex]\( (g - h)(x) \)[/tex] at [tex]\( x = -8 \)[/tex]:

The expression [tex]\( (g - h)(x) \)[/tex] denotes the difference between [tex]\( g(x) \)[/tex] and [tex]\( h(x) \)[/tex]. Thus:
[tex]\[ (g - h)(x) = g(x) - h(x) \][/tex]

Substitute [tex]\( x = -8 \)[/tex]:
[tex]\[ (g - h)(-8) = g(-8) - h(-8) = 3 - (-1) = 3 + 1 = 4 \][/tex]

So, the value of [tex]\( (g - h)(-8) \)[/tex] is 4.

Therefore, the solution to the question is:
[tex]\[ (g-h)(-8) = 4 \][/tex]

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