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# What are the domain and range of the function?

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What are the domain and range of the function?

f(x)= 1/3x7 Jan 12, 2018

#1
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Assuming that     f(x)  =  1 / (3x7)

Any  x  value that makes the denominator zero is excluded from the domain.

Let's find any excluded  x  value.

3x7  =   0          Divide both sides by  3 .

x7   =   0          Take the  7th  root of both sides.

x     =   0

So the only excluded  x  value is  0 . So the domain is  (-∞, 0) U (0, ∞)

No matter how big or small of an  x  we plug in,  f(x)  cannot be zero.

The range is (-∞, 0) U (0, ∞)

Here's a graph of the function.

Jan 12, 2018
edited by hectictar  Jan 12, 2018

#1
+1

Assuming that     f(x)  =  1 / (3x7)

Any  x  value that makes the denominator zero is excluded from the domain.

Let's find any excluded  x  value.

3x7  =   0          Divide both sides by  3 .

x7   =   0          Take the  7th  root of both sides.

x     =   0

So the only excluded  x  value is  0 . So the domain is  (-∞, 0) U (0, ∞)

No matter how big or small of an  x  we plug in,  f(x)  cannot be zero.

The range is (-∞, 0) U (0, ∞)

Here's a graph of the function.

hectictar Jan 12, 2018
edited by hectictar  Jan 12, 2018