Whats the answer it would be kind if someone told me

Algebraically find the inverse of a function

Savatey [412]

9514 1404 393

Answer:

1) f⁻¹(x) = 6 ± 2√(x -1)

3) y = (x +4)² -2

5) y = (x -4)³ -4

Step-by-step explanation:

In general, swap x and y, then solve for y. Quadratics, as in the first problem, do not have an inverse function: the inverse relation is double-valued, unless the domain is restricted. Here, we're just going to consider these to be "solve for ..." problems, without too much concern for domain or range.

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1) x = f(y)

x = (1/4)(y -6)² +1

4(x -1) = (y-6)² . . . . . . subtract 1, multiply by 4

±2√(x -1) = y -6 . . . . square root

y = 6 ± 2√(x -1) . . . . inverse relation

f⁻¹(x) = 6 ± 2√(x -1) . . . . in functional form

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3) x = √(y +2) -4

x +4 = √(y +2) . . . . add 4

(x +4)² = y +2 . . . . square both sides

y = (x +4)² -2 . . . . . subtract 2

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5) x = ∛(y +4) +4

x -4 = ∛(y +4) . . . . . subtract 4

(x -4)³ = y +4 . . . . . cube both sides

y = (x -4)³ -4 . . . . . . subtract 4

6 0

2 years ago

The data show the last 12 weeks of a

stira [4]

Answer:

A $60

Step-by-step explanation:

8 0

3 years ago

A competitive knitter is knitting a circular place mat. The radius of the mat is given by the formula

Ilia_Sergeevich [38]

Answer: A. $A'(t)=\frac{4356\pi}{(t+11)^{3}}-\frac{527076\pi}{(t+11)^{5}}$

B. A'(5) = 1.76 cm/s

Step-by-step explanation: Rate of change measures the slope of a curve at a certain instant, therefore, rate is the derivative.

A. Area of a circle is given by

$A=\pi.r^{2}$

So to find the rate of the area:

$\frac{dA}{dt}=\frac{dA}{dr}.\frac{dr}{dt}$

$\frac{dA}{dr} =2.\pi.r$

Using $r(t)=3-\frac{363}{(t+11)^{2}}$

$\frac{dr}{dt}=\frac{726}{(t+11)^{3}}$

Then

$\frac{dA}{dt}=2.\pi.r.[\frac{726}{(t+11)^{3}}]$

$\frac{dA}{dt}=2.\pi.[3-\frac{363}{(t+11)^{2}}].\frac{726}{(t+11)^{3}}$

Multipying and simplifying:

$\frac{dA}{dt}=\frac{4356\pi}{(t+11)^{3}} -\frac{527076\pi}{(t+11)^{5}}$

The rate at which the area is increasing is given by expression $A'(t)=\frac{4356\pi}{(t+11)^{3}} -\frac{527076\pi}{(t+11)^{5}}$ .

B. At t = 5, rate is:

$A'(5)=\frac{4356\pi}{(5+11)^{3}} -\frac{527076\pi}{(5+11)^{5}}$

$A'(5)=\frac{4356\pi}{4096} -\frac{527076\pi}{1048576}$

$A'(5)=\frac{2408693760\pi}{4294967296}$

$A'(5)=1.76268$

At 5 seconds, the area is expanded at a rate of 1.76 cm/s.

5 0

2 years ago

Which statement about the system of equations is true?

vagabundo [1.1K]

8x + 6y = 10 ----------- (1)
5x - 3y = 2.2 ---------- (2)

(2) x 2:
10 x - 6y = 4.4 --------(2a)

(2a) + (1)
18x = 14.4
x = 1.8 ------- sub into (1)
8 (1.8) + 6y = 10
14.4 + 6y = 10
6y = 10 - 14.4
6y = - 4.4
y = - 0.73

There is 1 set of solution to it. (Answer C)

3 0

2 years ago

Not sure if I did this correctly... please help 3. Is the one I'm kinda stuck on

denis23 [38]

You got the b part wrong. It would be 4B+4C/2=4D

6 0

2 years ago

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