QuestionFind the zeros of the function $f(x)=\sqrt{3x-1}-2$ using algebraic methods.

Studdy Solution

STEP 1

Assumptions1. We are looking for the zeros of the function $f(x)=\sqrt{3 x-1}-$ . . A zero of a function is a value of $x$ that makes the function equal to zero.

STEP 2

To find the zeros of the function, we need to solve the equation $f(x) =0$ . This gives us the equation $\sqrt{ x-1}-2 =0$

STEP 3

We can start solving this equation by isolating the square root on one side. We do this by adding2 to both sides of the equation.
$\sqrt{3 x-1} =2$

STEP 4

Next, we can get rid of the square root by squaring both sides of the equation. This gives us $(\sqrt{3 x-1})^2 =2^2$

STEP 5

implify the equation.
$3 x-1 =4$

STEP 6

Now, we can solve for $x$ by first adding1 to both sides of the equation.
$3 x =5$

STEP 7

Finally, divide both sides of the equation by3 to solve for $x$ .
$x = \frac{5}{3}$ So, the zero of the function $f(x)=\sqrt{3 x-1}-2$ is $x = \frac{5}{3}$ .

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QuestionFind the zeros of the function $f(x)=\sqrt{3x-1}-2$ using algebraic methods.

Studdy Solution

STEP 1

Assumptions1. We are looking for the zeros of the function $f(x)=\sqrt{3 x-1}-$ . . A zero of a function is a value of $x$ that makes the function equal to zero.

STEP 2

To find the zeros of the function, we need to solve the equation $f(x) =0$ . This gives us the equation $\sqrt{ x-1}-2 =0$

STEP 3

We can start solving this equation by isolating the square root on one side. We do this by adding2 to both sides of the equation.
$\sqrt{3 x-1} =2$

STEP 4

Next, we can get rid of the square root by squaring both sides of the equation. This gives us $(\sqrt{3 x-1})^2 =2^2$

STEP 5

implify the equation.
$3 x-1 =4$

STEP 6

Now, we can solve for $x$ by first adding1 to both sides of the equation.
$3 x =5$

STEP 7

Finally, divide both sides of the equation by3 to solve for $x$ .
$x = \frac{5}{3}$ So, the zero of the function $f(x)=\sqrt{3 x-1}-2$ is $x = \frac{5}{3}$ .

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QuestionFind the zeros of the function f(x)=3x−1−2f(x)=\sqrt{3x-1}-2f(x)=3x−1​−2 using algebraic methods.

Studdy Solution

STEP 1

Assumptions1. We are looking for the zeros of the function f(x)=3x−1−f(x)=\sqrt{3 x-1}-f(x)=3x−1​−. . A zero of a function is a value of xxx that makes the function equal to zero.

STEP 2

To find the zeros of the function, we need to solve the equation f(x)=0f(x) =0f(x)=0. This gives us the equationx−1−2=0\sqrt{ x-1}-2 =0x−1​−2=0

STEP 3

We can start solving this equation by isolating the square root on one side. We do this by adding2 to both sides of the equation.3x−1=2\sqrt{3 x-1} =23x−1​=2

STEP 4

Next, we can get rid of the square root by squaring both sides of the equation. This gives us(3x−1)2=22(\sqrt{3 x-1})^2 =2^2(3x−1​)2=22

STEP 5

implify the equation.3x−1=43 x-1 =43x−1=4

STEP 6

Now, we can solve for xxx by first adding1 to both sides of the equation.3x=53 x =53x=5

STEP 7

Finally, divide both sides of the equation by3 to solve for xxx.x=53x = \frac{5}{3}x=35​So, the zero of the function f(x)=3x−1−2f(x)=\sqrt{3 x-1}-2f(x)=3x−1​−2 is x=53x = \frac{5}{3}x=35​.

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QuestionFind the zeros of the function $f(x)=\sqrt{3x-1}-2$ using algebraic methods.

Assumptions1. We are looking for the zeros of the function $f(x)=\sqrt{3 x-1}-$ . . A zero of a function is a value of $x$ that makes the function equal to zero.

To find the zeros of the function, we need to solve the equation $f(x) =0$ . This gives us the equation $\sqrt{ x-1}-2 =0$

We can start solving this equation by isolating the square root on one side. We do this by adding2 to both sides of the equation.
$\sqrt{3 x-1} =2$

Next, we can get rid of the square root by squaring both sides of the equation. This gives us $(\sqrt{3 x-1})^2 =2^2$

implify the equation.
$3 x-1 =4$

Now, we can solve for $x$ by first adding1 to both sides of the equation.
$3 x =5$

Finally, divide both sides of the equation by3 to solve for $x$ .
$x = \frac{5}{3}$ So, the zero of the function $f(x)=\sqrt{3 x-1}-2$ is $x = \frac{5}{3}$ .