The correct answer is: Option 3: [tex](hofog)(x)=\frac{x-14}{x+4}[/tex]
Step-by-step explanation:
Given
[tex]f(x)=\frac{x-6}{x}\\g(x)=x+4\\h(x)=3x-2[/tex]
We have to find
[tex](hofog)(x)[/tex]
This will be equal to:
[tex]h(f(g(x)))[/tex]
So we have to find the composition of (fog)(x) first
[tex](fog)(x) = f(g(x))\\=\frac{x+4-6}{x+4}\\=\frac{x-2}{x+4}[/tex]
Now,
[tex](hofog)(x)=h(f(g(x)))\\=3(\frac{x-2}{x+4})-2\\=\frac{3x-6}{x+4}-2\\=\frac{3x-6-2(x+4)}{x+4}\\=\frac{3x-6-2x-8}{x+4}\\=\frac{x-14}{x+4}[/tex]
The correct answer is: Option 3: [tex](hofog)(x)=\frac{x-14}{x+4}[/tex]
Keywords: Composition, Functions
Learn more about function composition at:
- brainly.com/question/10015690
- brainly.com/question/10048445
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