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solniwko [45]
3 years ago
12

H(x)= 9/x( x^2-49) Determine the domain of the function

Mathematics
1 answer:
Norma-Jean [14]3 years ago
8 0

Answer: The domain of the function h(x) = \frac{9}{x(x^2-49)} is:

Interval Notation: (-∞ , -7) ∪ (-7 , 0) ∪ (0 , 7) ∪ (7, ∞)

Set-Builder Notation: { x | x ≠ 0 , 7 , -7 }

All real numbers besides 0, 7, and -7.

Step-by-step explanation:

In order to find the domain of your rational function, we need to simplify it:

h(x) = \frac{9}{x(x^2-49)} = \frac{9}{(x)(x+7)(x-7)}

Remember, most of the time, the domain of a rational function consists of all real numbers besides zero.

To find the domain, we equal the equations in the denominator to zero.

x=0

x+7=0 --> x=-7

x-7=0 --> x=7

So all real numbers except for 0, -7, and 7 are in the domain of this rational function.

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\angle GAB = cos^{-1} \left (\dfrac{36}{39}  \right )

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The height of the parallelogram = 120/13 =  9.23 in.

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