Question

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

(−[infinity], 2) (2, [infinity])

(−[infinity], −2) (−2, [infinity])

(−[infinity], 1) (1, [infinity])

(−[infinity], −1) (−1, [infinity])

Answer 1

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].