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2 years ago

Find the function !!! 10 points - Help needed!

Mathematics

2 answers:

Arte-miy333 [17]2 years ago

4 0

<h2>Hello!</h2>

The answer is:

The first option,

$f^{-1}(x)=\frac{x-2}{4}$

To find the inverse of a function, we need to rewrite the variable "x" with "y" and the variable "y" with "x", and then, isolate "y".

We are given the function:

$f(x)=4x+2$

Write "f(x)" is equal to write "y", so:

$y=4x+2$

Now, finding the inverse, we have:

$y=4x+2\\x=4y+2\\x-2=4y\\y=\frac{x-2}{4}$

Hence, we have that the answer is the first option,

$f^{-1}(x)=\frac{x-2}{4}$

Have a nice day!

ololo11 [35]2 years ago

4 0

ANSWER

${f}^{ - 1} (x) = \frac{x - 2}{4}$

EXPLANATION

The given function is

f(x)=4x+2

To find the inverse, we let

y=4x+2

Then, interchange x and y.

x=4y+2

Solve for y,

x-2=4y.

Divide both sides by 4

$y = \frac{x - 2}{4}$

Hence, the inverse is:

${f}^{ - 1} (x) = \frac{x - 2}{4}$

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If m(x) =x+5/x-1 and n(x) = x - 3, which function has the same domain as (mºn)(x)?

GREYUIT [131]

We have

M(X) = (X + 5)/(X - 1)

N(X) = X - 3

So,

M(N(X)) = [(X - 3) + 5]/[(X - 3) - 1]

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D = {X / X ≠ 4}

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2 years ago

Let u and v be the solutions to 3x^2 + 5x + 7 = 0. Find u/v+v/u

Hitman42 [59]

Answer: $\dfrac{-17}{21}$

Step-by-step explanation:

Given: u and v be are the solutions of $3x^2+5x+7=0$

Let $ax^2+bx+c=0$ is the quadratic equation and u and v are the zeroes/solutions then

Sum of zeroes; $u+v = \dfrac{-b}{a}$

Product of zeroes; $uv= \dfrac{c}{a}$

Comparing $3x^2+5x+7=0$ to $ax^2+bx+c=0$

we get a= 3 , b= 5 and c = 7

$u+v = \dfrac{-b}{a} = \dfrac{-5}{3}----(i)$

$uv= \dfrac{c}{a} = \dfrac{7}{3}----(ii)$

Now we have to find

$\dfrac{u}{v} +\dfrac{v}{u} =\dfrac{u^2+v^2}{uv}$ adding and subtracting 2uv in numerator we get

$= \dfrac{u^2+v^2+2uv-2uv}{uv}= \dfrac{(u+v)^2-2uv}{uv}$

Substituting the values from (i) and (ii) we get

$\dfrac{(\dfrac{-5}{3} )^2-2\times \dfrac{7}{3} }{\dfrac{7}{3} } = \dfrac{\dfrac{25}{9} -\dfrac{14}{3} }{\dfrac{7}{3} }= \dfrac{\dfrac{25-42}{9} }{\dfrac{7}{3}} =\dfrac{-17}{9} \times \dfrac{3}{7} = \dfrac{-17}{21}$

Hence, the value of $\dfrac{u}{v} +\dfrac{v}{u}$ is $\dfrac{-17}{21}$

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