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laiz [17]
4 years ago
6

Graph the inverse circular function by hand, given f(x) = 3sin(2x) ;-pi/4 ≤ ≤pi/4

Mathematics
1 answer:
nasty-shy [4]4 years ago
3 0

Part a)

a) The given function is

f(x) = 3 \sin(2x)

We let

y =  3 \sin(2x)

Interchange x and y.

x=  3 \sin(2y)

Solve for y;

\frac{x}{3}  =  \sin(2y)

y =  \frac{1}{2}  { \sin}^{ - 1}( \frac{x}{3} )

{f}^{ - 1}(x)  =  \frac{1}{2}  { \sin}^{ - 1}( \frac{x}{3} )

Part b) The range of f(x) refers to y-values for which f(x) exists.

The range of f(x) is

-  3 \leqslant y \leqslant 3

This is because the function is within y=-3 and y=3.

c) The range of

{f}^{ - 1} (x)

is

-  \frac{ \pi}{4}  \leqslant y \leqslant  \frac{\pi}{4}

The domain is -3≤x≤3

This is because the domain and range of a function and its inverse swaps.

Part d) The graph is shown in the attachment.

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Elena L [17]

Responder:

3 / 4x + 1/2 = x

Explicación paso a paso:

Dado que:

Capacidad total = x

Volumen inicial = cierta fracción * capacidad total

Volumen adicional agregado para llenar = 1/2

Por eso,

Inicial. Volumen + volumen adicional = volumen total

De las opciones:

Un volumen inicial de 3 / 4x

Volumen adicional de 1/2

Volumen total = x

Sumar todo hace que la ecuación:

3 / 4x + 1/2 = x

x - 3 / 4x = 1/2

Por lo tanto, la ecuación correcta de la opción es: 3 / 4x + 1/2 = x

7 0
3 years ago
Find the slope of the line passing through the points (-7.6) and (-7.-2).​
snow_lady [41]

Answer:

Undefined

Step-by-step explanation:

the equation for slope is y2-y1/x2-x1

(-2-6)/(-7-(7))= -8/0

This would leave you with an undefined slope.

7 0
3 years ago
(2x^3+9x^2+x-12)/(x+4) simplify
neonofarm [45]

Answer:

<h2>2 {x}^{2}  + x - 3</h2>

Step-by-step explanation:

\frac{2 {x}^{3}  + 9 {x}^{2}  + x - 12}{x + 4}

Write 9 {x}^{2} as a sum

\frac{2 {x}^{3}  - 2 {x}^{2} + 11 {x}^{2}   + x - 12}{x + 4}

Write X as a sum

\frac{2 {x}^{3}  - 2 {x}^{2} + 11 {x}^{2} - 11x + 12x - 12  }{x + 4}

Factor out 2 {x}^{2} from the expression

\frac{2 {x}^{2}(x - 1) + 11 {x}^{2} -  11x + 12x - 12  }{x  + 4}

Factor out 11x from the expression

\frac{2 {x}^{2} (x - 1) + 11x(x - 1) + 12x - 12}{x + 4}

Factor out 12 from the expression

\frac{2 {x}^{2}(x - 1) + 11(x - 1)  + 12(x - 1) }{x + 4}

Factor out X - 1 from the expression

\frac{(x - 1)(2  {x}^{2}   + 11x + 12)}{x + 4}

Write 11x as a sum

\frac{(x - 1)(2 {x}^{2}  + 8x + 3x + 12)}{x + 4}

Factor out 2x from the expression

\frac{(x - 1)(2x(x + 4) + 3x + 12)}{x + 4}

Factor out 3 from the expression

\frac{(x - 1)(2x(x + 4) + 3(x  + 4)}{x + 4}

Factor out X + 4 from the expression

\frac{(x - 1)(x + 4)(2x + 3)}{x + 4}

Reduce the fraction with X + 4

(x - 1)(2x + 3)

Multiply the parantheses

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

Collect like terms

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Hope this helps...

Good luck on your assignment...

4 0
3 years ago
How big are soobins feet
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Answer:

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Step-by-step explanation:

i love soobin so much :')

3 0
4 years ago
Which graph is a translation of f(x) = x2 , according the rule:
bixtya [17]
For this case we have the following original function:
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 Answer:
 
Third graph
8 0
3 years ago
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