PLEASE HELP MEAN A LOT I WILL GIVE BRAINLIEST

Find g^-1(x) A B C D

Katyanochek1 [597]

<h2>Answer:</h2>

$a. \ g^{-1}=-1 \pm\sqrt{\frac{3}{x}+1}$

<h2>Step-by-step explanation:</h2>

A function has an inverse function if and only if passes the Horizontal Line Test for Inverse Functions. This test tells us that a function $f$ has an inverse function if and only if there is no any horizontal line that intersects the graph of $f$ at more than one point. So the function is called one-to-one. The graph of $g$ is shown below. As you can see, this function does not pass the Horizontal Line Test, therefore the inverse is not a function. However, let's find $g^-{1}(x)$ :

$g(x)=\frac{3}{x^2+2x} \\ \\ Substitute \ g(x) \ by \ y \\ \\y=\frac{3}{x^2+2x} \\ \\ Interchange \ x \ and \ y: \\ \\ x=\frac{3}{y^2+2y} \\ \\ Solve \ for \ y: \\ \\y^2+2y=\frac{3}{x} \\ \\ Completing \ square \\ \\y^2+2y\mathbf{+ 1}\mathbf{-1}=\frac{3}{x} \\ \\(y+1)^2=\frac{3}{x}+1 \\ \\y+1=\pm\sqrt{\frac{3}{x}+1} \\ \\ y=-1 \pm\sqrt{\frac{3}{x}+1}$

Finally, substitute $y \ by \ g^{-1}$ :

$boxed{g^{-1}=-1 \pm\sqrt{\frac{3}{x}+1}}$

7 0

3 years ago

Which of the following is a third root of the given complex number? 27(cos(pi/5)+isin(pi/5))

Digiron [165]

The third root of the given complex number 27(cos(pi/5)+isin(pi/5)) is 3(cos(pi/15)+i sin(pi/15))

The solution would be like this for this specific problem: 2^5 = 32 so you need a 2 out front the 5th root of cos(x) + i sin(x) is cos(x/5) + i sin(x/5). Additionally, 5 roots are located at even intervals around the circle. They are spaced every 2 pi/5 or 6 pi/15 radians. Roots are located at pi/15, pi/15+ 10pi/15 = 11 pi/15 and pi/15+ 20pi/15 = 21 pi/15 (or 7 pi /5 ).

5 0

4 years ago

Which expression is the result of factoring the expression below by taking out its greatest common factor? 16x^2-8x=? Choose 1 a

Natasha2012 [34]

Answer:

I think it is A

Step-by-step explanation:

8 0

3 years ago

Kesha threw her baton up in the air from the marching band platform during practice. The equation h(t) = −16t² + 54t + 40 gives

lapo4ka [179]

Answer:

a) 40 feet

b) 54 ft/min

c) 4 mins

Step-by-step explanation:

Solution:-

- Kesha models the height ( h ) of the baton from the ground level but thrown from a platform of height hi.

- The function h ( t ) is modeled to follow a quadratic - parabolic path mathematically expressed as:

h ( t ) = −16t² + 54t + 40

Which gives the height of the baton from ground at time t mins.

- The initial point is of the height of the platform which is at a height of ( hi ) from the ground level.

- So the initial condition is expressed by time = 0 mins, the height of the baton h ( t ) would be:

h ( 0 ) = hi = -16*(0)^2 + 54*0 + 40

h ( 0 ) = hi = 0 + 0 + 40 = 40 feet

Answer: The height of the platform hi is 40 feet.

- The speed ( v ) during the parabolic path of the baton also varies with time t.

- The function of speed ( v ) with respect to time ( t ) can be determined by taking the derivative of displacement of baton from ground with respect to time t mins.

v ( t ) = dh / dt

v ( t )= d ( −16t² + 54t + 40 ) / dt

v ( t )= -2*(16)*t + 54

v ( t )= -32t + 54

- The velocity with which Kesha threw the baton is represented by tim t = 0 mins.

Hence,

v ( 0 ) = vi = -32*( 0 ) + 54

v ( 0 ) = vi = 54 ft / min

Answer: Kesha threw te baton with an initial speed of vo = 54 ft/min

- The baton reaches is maximum height h_max and comes down when all the kinetic energy is converted to potential energy. The baton starts to come down and cross the platform height hi = 40 feet and hits the ground.

- The height of the ball at ground is zero. Hence,

h ( t ) = 0

0 = −16t² + 54t + 40

0 = -8t^2 + 27t + 20

- Use the quadratic formula to solve the quadratic equation:

$t = \frac{27+/-\sqrt{27^2 - 4*8*(-20)} }{2*8}\\\\t = \frac{27+/-\sqrt{1369} }{16}\\\\t = \frac{27+/-37 }{16}\\\\t = \frac{27 + 37}{16} \\\\t = 4$

Answer: The time taken for the baton to hit the ground is t = 4 mins

3 0

3 years ago

Simplify the following expression (x+y)²

MrMuchimi

Answer:

${x}^{2} + 2xy + {y}^{2}$

Step-by-step explanation:

1) Use square sum: (a + b)² = a² + 2ab + b².

${x}^{2} + 2xy + y^{2}$

Therefor, the answer is x² + 2xy + y².

8 0

3 years ago