QuestionDetermine where the function $f(x)=\frac{x+1}{x^{3}-x}$ is undefined by finding the values of $x$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=\frac{x+1}{x^{3}-x}$ . We need to find the values of $x$ for which the function is undefined.

STEP 2

A function is undefined when the denominator of a fraction is equal to zero. So, we need to find the values of $x$ that make the denominator of the function equal to zero.
$x^{}-x=0$

STEP 3

We can factor out an $x$ from the equation to simplify it.
$x(x^{2}-1)=0$

STEP 4

The equation $x^{2}-1=0$ is a difference of squares, which can be factored as $(x-1)(x+1)$ .
So, the factored form of the equation is $x(x-1)(x+1)=0$

STEP 5

Setting each factor equal to zero gives the solutions for $x$ .
$x=0, x-1=0, x+1=0$

STEP 6

olving the above equations for $x$ gives $x=0, x=1, x=-1$ So, the function $f(x)=\frac{x+1}{x^{3}-x}$ is undefined for $x=0$ , $x=1$ , and $x=-1$ .

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QuestionDetermine where the function $f(x)=\frac{x+1}{x^{3}-x}$ is undefined by finding the values of $x$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=\frac{x+1}{x^{3}-x}$ . We need to find the values of $x$ for which the function is undefined.

STEP 2

A function is undefined when the denominator of a fraction is equal to zero. So, we need to find the values of $x$ that make the denominator of the function equal to zero.
$x^{}-x=0$

STEP 3

We can factor out an $x$ from the equation to simplify it.
$x(x^{2}-1)=0$

STEP 4

The equation $x^{2}-1=0$ is a difference of squares, which can be factored as $(x-1)(x+1)$ .
So, the factored form of the equation is $x(x-1)(x+1)=0$

STEP 5

Setting each factor equal to zero gives the solutions for $x$ .
$x=0, x-1=0, x+1=0$

STEP 6

olving the above equations for $x$ gives $x=0, x=1, x=-1$ So, the function $f(x)=\frac{x+1}{x^{3}-x}$ is undefined for $x=0$ , $x=1$ , and $x=-1$ .

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QuestionDetermine where the function f(x)=x+1x3−xf(x)=\frac{x+1}{x^{3}-x}f(x)=x3−xx+1​ is undefined by finding the values of xxx.

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=x+1x3−xf(x)=\frac{x+1}{x^{3}-x}f(x)=x3−xx+1​ . We need to find the values of xxx for which the function is undefined.

STEP 2

A function is undefined when the denominator of a fraction is equal to zero. So, we need to find the values of xxx that make the denominator of the function equal to zero.x−x=0x^{}-x=0x−x=0

STEP 3

We can factor out an xxx from the equation to simplify it.x(x2−1)=0x(x^{2}-1)=0x(x2−1)=0

STEP 4

The equation x2−1=0x^{2}-1=0x2−1=0 is a difference of squares, which can be factored as (x−1)(x+1)(x-1)(x+1)(x−1)(x+1).So, the factored form of the equation isx(x−1)(x+1)=0x(x-1)(x+1)=0x(x−1)(x+1)=0

STEP 5

Setting each factor equal to zero gives the solutions for xxx.x=0,x−1=0,x+1=0x=0, x-1=0, x+1=0x=0,x−1=0,x+1=0

STEP 6

olving the above equations for xxx givesx=0,x=1,x=−1x=0, x=1, x=-1x=0,x=1,x=−1So, the function f(x)=x+1x3−xf(x)=\frac{x+1}{x^{3}-x}f(x)=x3−xx+1​ is undefined for x=0x=0x=0, x=1x=1x=1, and x=−1x=-1x=−1.

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QuestionDetermine where the function $f(x)=\frac{x+1}{x^{3}-x}$ is undefined by finding the values of $x$ .

Assumptions1. The function is $f(x)=\frac{x+1}{x^{3}-x}$ . We need to find the values of $x$ for which the function is undefined.

A function is undefined when the denominator of a fraction is equal to zero. So, we need to find the values of $x$ that make the denominator of the function equal to zero.
$x^{}-x=0$

We can factor out an $x$ from the equation to simplify it.
$x(x^{2}-1)=0$

The equation $x^{2}-1=0$ is a difference of squares, which can be factored as $(x-1)(x+1)$ .
So, the factored form of the equation is $x(x-1)(x+1)=0$

Setting each factor equal to zero gives the solutions for $x$ .
$x=0, x-1=0, x+1=0$

olving the above equations for $x$ gives $x=0, x=1, x=-1$ So, the function $f(x)=\frac{x+1}{x^{3}-x}$ is undefined for $x=0$ , $x=1$ , and $x=-1$ .