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babymother [125]
3 years ago
9

One question please help!

Mathematics
2 answers:
SIZIF [17.4K]3 years ago
7 0

The domain of (f/g)(x) will be:   {x\in R : x>3}

<em><u>Explanation</u></em>

Given functions are:  f(x)= -\frac{1}{x} and g(x)=\sqrt{3x-9}

So...

(f/g)(x)= \frac{f(x)}{g(x)}= \frac{-\frac{1}{x}}{\sqrt{3x-9}}=-\frac{1}{x\sqrt{3x-9}}

As (f/g)(x) is in fraction form, so the denominator part can't be 0 for defining the function and as (3x-9) is under square root so the value of (3x-9) will be always greater than 0

Thus.....

x\neq 0\\ \\ or \\ \\ 3x-9>0\\ 3x>9\\ x>3

So the domain of (f/g)(x) will be:  {x\in R : x>3}

ss7ja [257]3 years ago
5 0

Question 1: Determine the domain of h(x)=\frac{5}{\sqrt{2x+10} } and write it using set builder notation.

Answer: <em>{x|x>-5}</em>

Question 2: Find the domain and range of the function shown in the graph. Write the domain and range using interval notation.

Answer: <em>domain: (-6, -1] ∪ (1, 5] </em>

<em>               range: (-3, 2] ∪ [3, 7)</em>

Question 3: Find (f*g)(x) when f(x)=\frac{\sqrt{x+3} }{x} and g(x)= \frac{\sqrt{x+3} }{2x}

Answer: <em>\frac{x+3}{2x^{2} }</em>

Question 4: Determine the domain of (f/g)(x) when f(x)=\frac{-1}{x} and g(x)=\sqrt{3x-9}

Answer: <em>(3,∞)</em>

.

. For more answers follow this link to my quizlet Lemon_Milk

.                                         https://quizlet.com/_6xjh07

.

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