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lesya [120]
3 years ago
10

Find the domain of (f/g)(x) when f(x)=1/x and g(x)=square root x+8

Mathematics
2 answers:
nadezda [96]3 years ago
7 0
<h2>Answer:</h2>

The domain of the given function is:

              x>-8\ \text{and}\ x\neq 0

<h2>Step-by-step explanation:</h2>

Domain of a function--

The domain of a function is the set of all the x-values i.e. the value of the independent variable for which a function is well defined.

We have a function f(x) and g(x) as follows:

f(x)=\dfrac{1}{x}\\\\g(x)=\sqrt{x+8}

Hence,

(\dfrac{f}{g})(x)=\dfrac{1}{x\sqrt{x+8}}

Now, we know that this function is well defined when the denominator quantity is defined and also when the denominator quantity is non-zero.

This means that:

          x\neq 0

and

\sqrt{x+8}\neq 0

i.e.

x\neq -8

Now we know that the square root function is defined when the radicand is greater than zero.

i.e.

x+8\geq 0\\\\x\geq -8

But x\neq -8

This means that:

x>-8

Hence, the domain is:

                       x>-8\ \text{and}\ x\neq 0

Alex_Xolod [135]3 years ago
6 0

Step-by-step explanation:

all work is pictured/shown

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