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Asked Sep 27, 2019
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GRAPHS AND FUNCTIONS
Domain of a rational function: Interval notation
The functions fand g are defined as follows.
х-1
f(x)
2
x2x1
х-7
g (x)
2
х* - Зх-28
For each function, find the domain.
Write each answer as an interval or union of intervals.
- CO
Domain of f
||
(O (0
0.O)
OUO
Domain of g :
X
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GRAPHS AND FUNCTIONS Domain of a rational function: Interval notation The functions fand g are defined as follows. х-1 f(x) 2 x2x1 х-7 g (x) 2 х* - Зх-28 For each function, find the domain. Write each answer as an interval or union of intervals. - CO Domain of f || (O (0 0.O) OUO Domain of g : X

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Expert Answer

Step 1

Given functions f(x) ang (x) defined as

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х-7 х-1 and g(x) - ҳ2_3х-28 f(x) - 2+2х+1

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Step 2

To find: Domain of the functions.

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a) We know that f(x) is defined when the denominator is not equal to 0. So, we eliminate all the values of x for which the denominator is 0. i.e. x2 2x 1 = 0 (x 1)20 x+1 0 1 X Thus, the domain of f(x) is -o, -1)U-1, o

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Step 3

Next,

...
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b) Similarly, we eliminate all the values of x for which the denominator of g(x) is o. i.e. x2 3x 28 = 0 x27x 4x - 28 (x 7)(x4) = 0 x- 7 = 0 or 0 x+ 4 = 0 x = -4,7 Thus, the domain of g(x) is o, -4)U(-4, 7)U (7, o)

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Tagged in
MathCalculus

Functions