Question

Please help. Not sure how to do this one

Answer 1

The correct answer is: Option 3: $(hofog)(x)=\frac{x-14}{x+4}$

Step-by-step explanation:

Given

$f(x)=\frac{x-6}{x}\\g(x)=x+4\\h(x)=3x-2$

We have to find

$(hofog)(x)$

This will be equal to:

$h(f(g(x)))$

So we have to find the composition of (fog)(x) first

$(fog)(x) = f(g(x))\\=\frac{x+4-6}{x+4}\\=\frac{x-2}{x+4}$

Now,

$(hofog)(x)=h(f(g(x)))\\=3(\frac{x-2}{x+4})-2\\=\frac{3x-6}{x+4}-2\\=\frac{3x-6-2(x+4)}{x+4}\\=\frac{3x-6-2x-8}{x+4}\\=\frac{x-14}{x+4}$

The correct answer is: Option 3: $(hofog)(x)=\frac{x-14}{x+4}$

Keywords: Composition, Functions

Learn more about function composition at:

• brainly.com/question/10015690
• brainly.com/question/10048445

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