QuestionEncuentra $\mu$ si $f(3 x-4)=4 x-10$ y $f(\mu)=2$ . ¿Cuál es el valor de $\mu$ ?

Studdy Solution

STEP 1

Assumptions1. The function $f \mathbb{R} \rightarrow \mathbb{R}$ is given by $f(3 x-4)=4 x-10$ . . It is given that $f(\mu)=$ .
3. We need to find the value of $\mu$ .

STEP 2

We know that $f(\mu)=2$ . We can substitute $x-4$ in place of $\mu$ in the equation, since $f(x-4)=4x-10$ is given.
$f(x-4)=2$

STEP 3

Now, we can equate this to the given equation $f(3x-)=x-10$ .
$x-10=2$

STEP 4

We can now solve this equation for $x$ . First, add10 to both sides of the equation.
$4x-10+10=2+10$

STEP 5

implify the equation.
$4x=12$

STEP 6

Now, divide both sides of the equation by4 to solve for $x$ .
$x=\frac{12}{4}$

STEP 7

Calculate the value of $x$ .
$x=3$

STEP 8

Now, we have the value of $x$ . But we need to find the value of $\mu$ , and we know that $\mu=3x-4$ .
$\mu=3x-4$

STEP 9

Substitute the value of $x$ into the equation.
$\mu=3(3)-4$

STEP 10

Calculate the value of $\mu$ .
$\mu=9-4=5$ So, $\mu=5$ .

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QuestionEncuentra $\mu$ si $f(3 x-4)=4 x-10$ y $f(\mu)=2$ . ¿Cuál es el valor de $\mu$ ?

Studdy Solution

STEP 1

Assumptions1. The function $f \mathbb{R} \rightarrow \mathbb{R}$ is given by $f(3 x-4)=4 x-10$ . . It is given that $f(\mu)=$ .
3. We need to find the value of $\mu$ .

STEP 2

We know that $f(\mu)=2$ . We can substitute $x-4$ in place of $\mu$ in the equation, since $f(x-4)=4x-10$ is given.
$f(x-4)=2$

STEP 3

Now, we can equate this to the given equation $f(3x-)=x-10$ .
$x-10=2$

STEP 4

We can now solve this equation for $x$ . First, add10 to both sides of the equation.
$4x-10+10=2+10$

STEP 5

implify the equation.
$4x=12$

STEP 6

Now, divide both sides of the equation by4 to solve for $x$ .
$x=\frac{12}{4}$

STEP 7

Calculate the value of $x$ .
$x=3$

STEP 8

Now, we have the value of $x$ . But we need to find the value of $\mu$ , and we know that $\mu=3x-4$ .
$\mu=3x-4$

STEP 9

Substitute the value of $x$ into the equation.
$\mu=3(3)-4$

STEP 10

Calculate the value of $\mu$ .
$\mu=9-4=5$ So, $\mu=5$ .

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QuestionEncuentra μ\muμ si f(3x−4)=4x−10f(3 x-4)=4 x-10f(3x−4)=4x−10 y f(μ)=2f(\mu)=2f(μ)=2. ¿Cuál es el valor de μ\muμ?

Studdy Solution

STEP 1

Assumptions1. The function fR→Rf \mathbb{R} \rightarrow \mathbb{R}fR→R is given by f(3x−4)=4x−10f(3 x-4)=4 x-10f(3x−4)=4x−10. . It is given that f(μ)=f(\mu)=f(μ)=.3. We need to find the value of μ\muμ.

STEP 2

We know that f(μ)=2f(\mu)=2f(μ)=2. We can substitute x−4x-4x−4 in place of μ\muμ in the equation, since f(x−4)=4x−10f(x-4)=4x-10f(x−4)=4x−10 is given.f(x−4)=2f(x-4)=2f(x−4)=2

STEP 3

Now, we can equate this to the given equation f(3x−)=x−10f(3x-)=x-10f(3x−)=x−10.x−10=2x-10=2x−10=2

STEP 4

We can now solve this equation for xxx. First, add10 to both sides of the equation.4x−10+10=2+104x-10+10=2+104x−10+10=2+10

STEP 5

implify the equation.4x=124x=124x=12

STEP 6

Now, divide both sides of the equation by4 to solve for xxx.x=124x=\frac{12}{4}x=412​

STEP 7

Calculate the value of xxx.x=3x=3x=3

STEP 8

Now, we have the value of xxx. But we need to find the value of μ\muμ, and we know that μ=3x−4\mu=3x-4μ=3x−4.μ=3x−4\mu=3x-4μ=3x−4

STEP 9

Substitute the value of xxx into the equation.μ=3(3)−4\mu=3(3)-4μ=3(3)−4

STEP 10

Calculate the value of μ\muμ.μ=9−4=5\mu=9-4=5μ=9−4=5So, μ=5\mu=5μ=5.

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QuestionEncuentra $\mu$ si $f(3 x-4)=4 x-10$ y $f(\mu)=2$ . ¿Cuál es el valor de $\mu$ ?

Assumptions1. The function $f \mathbb{R} \rightarrow \mathbb{R}$ is given by $f(3 x-4)=4 x-10$ . . It is given that $f(\mu)=$ .
3. We need to find the value of $\mu$ .

We know that $f(\mu)=2$ . We can substitute $x-4$ in place of $\mu$ in the equation, since $f(x-4)=4x-10$ is given.
$f(x-4)=2$

Now, we can equate this to the given equation $f(3x-)=x-10$ .
$x-10=2$

We can now solve this equation for $x$ . First, add10 to both sides of the equation.
$4x-10+10=2+10$

implify the equation.
$4x=12$

Now, divide both sides of the equation by4 to solve for $x$ .
$x=\frac{12}{4}$

Calculate the value of $x$ .
$x=3$

Now, we have the value of $x$ . But we need to find the value of $\mu$ , and we know that $\mu=3x-4$ .
$\mu=3x-4$

Substitute the value of $x$ into the equation.
$\mu=3(3)-4$

Calculate the value of $\mu$ .
$\mu=9-4=5$ So, $\mu=5$ .