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viktelen [127]
3 years ago
14

Consider he function f(x)=2x-4 a.find the inverse of (x) and name it g(x) . Show your work <br /><br /> B. Use funct

ion composition to show that f(x) and g(x) are inverses to each other. Please show work
Mathematics
1 answer:
inna [77]3 years ago
6 0

A.\\f(x)=2x-4\to y=2x-4\\\\\text{change x to y and y to x}\\\\x=2y-4\\\\\text{solve for y}\\\\2y-4=x\qquad|+4\\\\2y=x+4\qquad|:2\\\\y=\dfrac{1}{2}x+2\\\\f^{-1}(x)=g(x)=\dfrac{1}{2}x+2\\B.\\\text{Verifying if two functions are inverses of each other is a simple two-step process.}\\1.\ \text{Plug}\ f(x)\ \text{into}\ g(x)\ \text{and simplify}\\2.\  \text{Plug}\ g(x)\ \text{into}\ f(x)\ \text{and simplify}\\\\If\ g[f(x)]=f[g(x)]=x,\ then\ functions\ are\ inverses\ of\ each\ other.

f(x)=2x-4,\ g(x)=\dfrac{1}{2}x+2\\\\g[f(x)]=\dfrac{1}{2}(2x-4)+2=\dfrac{1}{2}(2x)+\dfrac{1}{2}(-4)+2=x-2+2=x\\\\f[g(x)]=2\left(\dfrac{1}{2}x+2\right)-4=2\left(\dfrac{1}{2}x\right)+2(2)-4=x+4-4=x\\\\\text{Since the results above came out OK, both}\ x,\text{ then we can claim}\\\text{that functions f (x) and g (x) are inverses of each other.}

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Three circles with centers A, B, and C are externally tangent to each other as shown in the figure. Lines EG and DG are tangent
fiasKO [112]
My solution to the problem is as follows:

EC = 15 ... draw CF = 6 (radius) ...use Pythagorean theorem to find EF. 

EF^2 + CF^2 = EC^2 
EF^2 = 15^2 - 6^2 = 189 .... EF = sq root 189 

triangle GDE is similar to CFE ... thus proportional 
GD / ED = CF / EF 
GD / 18 = 6 / (sq root 189) 
<span>GD = 108 / (sq root 189)

I hope my answer has come to your help. God bless and have a nice day ahead!


</span>
5 0
3 years ago
Dividing Polynomials with Tables Isiah is dividing 2x3 - x2 + 2x + 5 by x + 1 using a division table. His work is shown here. Wh
lukranit [14]

Answer:

5

Step-by-step explanation:

We are asked to find the value of A. We know from the question that we need to have the sum of -3x and (A)x equal the third term of the original polynomial, which is 2x. written out in an equation, it looks like this.

-3x+(A)x=2x

We can simplify the equation if we add 3x to both sides, which then leaves us with this.

(A)x=5x

We can further simplify the equation by dividing both sides by x. This leaves us with our last equation for this problem.

A=5

Finally, we have our answer. We can also verify that this is a valid integer by multiplying our, now completed, quotient by the divisor and adding the remainder, which in this case, our remainder is 0, so we will not be including it in our operation.

(x+1)(2x^{2}-3x+5)

If our calculations were all correct, the product of these polynomials should equal our dividend, verifying our integer is valid; lo' and behold, it is.

2x^{3}-x^{2}+2x+5

8 0
3 years ago
La siguiente tabla presenta las frecuencias absolutas y relativas de las distintas caras de un dado cuando se simulan 300 lanzam
noname [10]

La opinión correcta es la de Camila que argumenta que la frecuencia relativa de la cara con el #6 será un valor cercano a 0,166.

<h3>Qué es la frecuencia relativa?</h3>

La frecuencia relativa es un término matemático que se utiliza en la estadística para referirse al número de veces que un evento se repite durante un experimento.

Por otra parte, es necesario aclara que la frecuencia relativa no se modifica en gran medida si se aumenta el número de veces de una prueba, debido a que la probabilidad de ocurrencia de este evento va a ser la misma.

De acuerdo a lo anterior, Camila tiene razón debido a que considera que el valor de la frecuencia relativa no se modifica en gran medida entre 300 o 600 lanzamientos de los dados.

Nota: Esta pregunta está incompleta porque no está la tabla. No obstante, la puedo responder basado en mi conocimiento previo.

Aprenda más sobre probabilidad en: brainly.com/question/16019390

6 0
2 years ago
Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for t
Olin [163]

Answer:

+- 10n

Step-by-step explanation:

✯Hello✯

↪  We need to work out the nth term rule

↪  We can do this by finding the differences between the numbers and using the rules

2A

3A+B

A+B+C

↪  (Sorry I cant draw a table for you)

↪  Using the rules and drawing a table we get the final answer

+- 10N

❤Gianna❤

8 0
3 years ago
Measure of angle A???
Rudik [331]

Answer:

A

Step-by-step explanation:

The triangle shown has all 3 sides equal in length, hence it is an equilateral triangle.

A property of equilateral triangles is the angles are congruent.

The sum of the 3 angles = 180°, hence the measure of each angle is

\frac{180}{3} = 60° → A


4 0
3 years ago
Read 2 more answers
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