QuestionFind the x-intercepts of the function $f(x)=\frac{x^{2}+2}{x^{2}+9x+9}$ .

Studdy Solution

STEP 1

Assumptions1. The function is given as $f(x)=\frac{x^{}+}{x^{}+9 x+9}$ . We are asked to find the x-intercepts of the function

STEP 2

The x-intercepts of a function are the values of x for which the function equals zero. We can find these by setting the function equal to zero and solving for x.
$f(x) =0$

STEP 3

Substitute the given function into the equation.
$\frac{x^{2}+2}{x^{2}+9 x+9} =0$

STEP 4

A fraction equals zero when the numerator is zero. So, we set the numerator of the function equal to zero and solve for x.
$x^{2}+2 =0$

STEP 5

Subtract2 from both sides of the equation to isolate $x^2$ .
$x^{2} = -2$

STEP 6

Take the square root of both sides to solve for x. Remember that the square root of a number has two solutions one positive and one negative.
$x = \pm \sqrt{-2}$

STEP 7

The square root of a negative number is an imaginary number. Therefore, the x-intercepts of the function are imaginary.
The function $f(x)=\frac{x^{2}+2}{x^{2}+9 x+9}$ does not have any real x-intercepts.

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QuestionFind the x-intercepts of the function $f(x)=\frac{x^{2}+2}{x^{2}+9x+9}$ .

Studdy Solution

STEP 1

Assumptions1. The function is given as $f(x)=\frac{x^{}+}{x^{}+9 x+9}$ . We are asked to find the x-intercepts of the function

STEP 2

The x-intercepts of a function are the values of x for which the function equals zero. We can find these by setting the function equal to zero and solving for x.
$f(x) =0$

STEP 3

Substitute the given function into the equation.
$\frac{x^{2}+2}{x^{2}+9 x+9} =0$

STEP 4

A fraction equals zero when the numerator is zero. So, we set the numerator of the function equal to zero and solve for x.
$x^{2}+2 =0$

STEP 5

Subtract2 from both sides of the equation to isolate $x^2$ .
$x^{2} = -2$

STEP 6

Take the square root of both sides to solve for x. Remember that the square root of a number has two solutions one positive and one negative.
$x = \pm \sqrt{-2}$

STEP 7

The square root of a negative number is an imaginary number. Therefore, the x-intercepts of the function are imaginary.
The function $f(x)=\frac{x^{2}+2}{x^{2}+9 x+9}$ does not have any real x-intercepts.

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QuestionFind the x-intercepts of the function f(x)=x2+2x2+9x+9f(x)=\frac{x^{2}+2}{x^{2}+9x+9}f(x)=x2+9x+9x2+2​.

Studdy Solution

STEP 1

Assumptions1. The function is given as f(x)=x+x+9x+9f(x)=\frac{x^{}+}{x^{}+9 x+9}f(x)=x+9x+9x+​ . We are asked to find the x-intercepts of the function

STEP 2

The x-intercepts of a function are the values of x for which the function equals zero. We can find these by setting the function equal to zero and solving for x.f(x)=0f(x) =0f(x)=0

STEP 3

Substitute the given function into the equation.x2+2x2+9x+9=0\frac{x^{2}+2}{x^{2}+9 x+9} =0x2+9x+9x2+2​=0

STEP 4

A fraction equals zero when the numerator is zero. So, we set the numerator of the function equal to zero and solve for x.x2+2=0x^{2}+2 =0x2+2=0

STEP 5

Subtract2 from both sides of the equation to isolate x2x^2x2.x2=−2x^{2} = -2x2=−2

STEP 6

Take the square root of both sides to solve for x. Remember that the square root of a number has two solutions one positive and one negative.x=±−2x = \pm \sqrt{-2}x=±−2​

STEP 7

The square root of a negative number is an imaginary number. Therefore, the x-intercepts of the function are imaginary.The function f(x)=x2+2x2+9x+9f(x)=\frac{x^{2}+2}{x^{2}+9 x+9}f(x)=x2+9x+9x2+2​ does not have any real x-intercepts.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the x-intercepts of the function $f(x)=\frac{x^{2}+2}{x^{2}+9x+9}$ .

Assumptions1. The function is given as $f(x)=\frac{x^{}+}{x^{}+9 x+9}$ . We are asked to find the x-intercepts of the function

The x-intercepts of a function are the values of x for which the function equals zero. We can find these by setting the function equal to zero and solving for x.
$f(x) =0$

Substitute the given function into the equation.
$\frac{x^{2}+2}{x^{2}+9 x+9} =0$

A fraction equals zero when the numerator is zero. So, we set the numerator of the function equal to zero and solve for x.
$x^{2}+2 =0$

Subtract2 from both sides of the equation to isolate $x^2$ .
$x^{2} = -2$

Take the square root of both sides to solve for x. Remember that the square root of a number has two solutions one positive and one negative.
$x = \pm \sqrt{-2}$

The square root of a negative number is an imaginary number. Therefore, the x-intercepts of the function are imaginary.
The function $f(x)=\frac{x^{2}+2}{x^{2}+9 x+9}$ does not have any real x-intercepts.