QuestionFind the domain of the function $f(x)=\frac{1}{x-2}$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=\frac{1}{x-}$

STEP 2

The domain of a function is the set of all possible input values (often the "x" variable), which produce a valid output from a particular function.

STEP 3

For the given function, the denominator cannot be equal to zero because division by zero is undefined in mathematics. Therefore, we need to find the value of $x$ that makes the denominator zero.
$x -2 =0$

STEP 4

olving the equation $x -2 =0$ for $x$ gives us $x =2$

STEP 5

So, the value $x =2$ is not in the domain of the function because it makes the denominator zero.

STEP 6

Therefore, the domain of the function $f(x)=\frac{1}{x-2}$ is all real numbers except $2$ . In interval notation, this can be written as $(-\infty,2) \cup (2, \infty)$ The domain of the function is all real numbers except $2$ .

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QuestionFind the domain of the function $f(x)=\frac{1}{x-2}$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=\frac{1}{x-}$

STEP 2

The domain of a function is the set of all possible input values (often the "x" variable), which produce a valid output from a particular function.

STEP 3

For the given function, the denominator cannot be equal to zero because division by zero is undefined in mathematics. Therefore, we need to find the value of $x$ that makes the denominator zero.
$x -2 =0$

STEP 4

olving the equation $x -2 =0$ for $x$ gives us $x =2$

STEP 5

So, the value $x =2$ is not in the domain of the function because it makes the denominator zero.

STEP 6

Therefore, the domain of the function $f(x)=\frac{1}{x-2}$ is all real numbers except $2$ . In interval notation, this can be written as $(-\infty,2) \cup (2, \infty)$ The domain of the function is all real numbers except $2$ .

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QuestionFind the domain of the function f(x)=1x−2f(x)=\frac{1}{x-2}f(x)=x−21​.

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=1x−f(x)=\frac{1}{x-}f(x)=x−1​

STEP 2

The domain of a function is the set of all possible input values (often the "x" variable), which produce a valid output from a particular function.

STEP 3

For the given function, the denominator cannot be equal to zero because division by zero is undefined in mathematics. Therefore, we need to find the value of xxx that makes the denominator zero.x−2=0x -2 =0x−2=0

STEP 4

olving the equation x−2=0x -2 =0x−2=0 for xxx gives usx=2x =2x=2

STEP 5

So, the value x=2x =2x=2 is not in the domain of the function because it makes the denominator zero.

STEP 6

Therefore, the domain of the function f(x)=1x−2f(x)=\frac{1}{x-2}f(x)=x−21​ is all real numbers except 222. In interval notation, this can be written as(−∞,2)∪(2,∞)(-\infty,2) \cup (2, \infty)(−∞,2)∪(2,∞)The domain of the function is all real numbers except 222.

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QuestionFind the domain of the function $f(x)=\frac{1}{x-2}$ .

Assumptions1. The function is $f(x)=\frac{1}{x-}$

For the given function, the denominator cannot be equal to zero because division by zero is undefined in mathematics. Therefore, we need to find the value of $x$ that makes the denominator zero.
$x -2 =0$

olving the equation $x -2 =0$ for $x$ gives us $x =2$

So, the value $x =2$ is not in the domain of the function because it makes the denominator zero.

Therefore, the domain of the function $f(x)=\frac{1}{x-2}$ is all real numbers except $2$ . In interval notation, this can be written as $(-\infty,2) \cup (2, \infty)$ The domain of the function is all real numbers except $2$ .