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Natasha2012 [34]
3 years ago
7

Find the domain for the rational function f of x equals quantity x plus 1 end quantity divided by quantity x minus 2 end quantit

y.
(−[infinity], 2) (2, [infinity])

(−[infinity], −2) (−2, [infinity])

(−[infinity], 1) (1, [infinity])

(−[infinity], −1) (−1, [infinity])
Mathematics
1 answer:
Elena L [17]3 years ago
7 0

Answer:

(- \infty, 2), (2, \infty)

Step-by-step explanation:

Given the function:

f(x) = \dfrac{x+1}{x-2}

To find:

Domain of the function.

Solution:

First of all, let us learn about definition of  domain of a function.

Domain of a function is the valid input values that can be provided to the function for which output is defined.

OR

Domain of a function f(x) are the values of x for which the output f(x) is a valid value.

i.e. The function does not tend to \infty or does not have \frac{0}0 form.

So, we will check for the values of x for which f(x) is not defined.

For value to tend to \infty, denominator will be 0.

x-2\neq 0 \\\Rightarrow x \neq 2

So, the domain can not have x = 2

Any other value of x does not have any undefined value for the function f(x).

Hence, the answer is:

\bold{(- \infty, 2), (2, \infty)}     [2 is not included in the domain].

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