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2 years ago

Determine algebraically whether f(x)=3x-2 and g(x)=(x+2)/3 are inverse functions. Show all work.

Mathematics

1 answer:

Sergio [31]2 years ago

4 0

Answer:

Yes

Step-by-step explanation:

f(x)=3 x-2

y= 3 x-2

x= 3y - 2

3 y -2 = x

3 y -2 + 2 = x + 2

3 y = x + 2

3 3 3

3 y = x + 2

3 3 3

y = x + 2 replace y with f ^ -1(x)

3 3

f ^-1 (x) = x + 2

3 3

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In 2000, the population of Big Springs was 13 thousand. Use the given doubling

trasher [3.6K]

Answer:

The answer is "26179.4".

Step-by-step explanation:

Assume year 2000 as t, that is t =0.

Formula:

$A= A_0e^{rt}$

Where,

$A_0 = \ initial \ pop \\\\r= \ rate \ in \ decimal \\\\t= \ time \ in \ year$

for doubling time,

$r = \frac{log (2)}{t} \\$

$r = \frac{\log (2)}{ 40} \\\\r= \frac{0.301}{40}\\\\r= 0.007$

Given value:

$A = A_0e^{rt} \\\\$

$A_0 = 13000$

$t= 40 \ years$

when year is 2000, t=0 so, year is 2100 year as t = 100.

$A = 13000 \times e^{et}\\\\A = 13000 \times e^{e \times t}\\\\A = 13000 \times e^{0.007 \times 100}\\\\A = 13000 \times e^{0.7}\\\\A= 13000\times 2.0138\\\\A = 26179.4$

7 0

2 years ago

What do you call the absolute values of 6 and -6

coldgirl [10]

I believe they are called opposites.

3 0

3 years ago

Miles is saving to buy a new car. He currently has $600 in his savings account. He plans on depositing $200 a month until he has

Marizza181 [45]

Answer:

7 months

Step-by-step explanation:

He plans on depositing $200 every month into the savings account that already has $600 in it.

We can represent the amount of money he will have after a certain number of months (x) as:

A = 600 + 200x

He needs to save $2000. Therefore, to find the months he needs to save, we need to find x when A is $2000:

2000 = 600 + 200x

200x = 2000 - 600

200x = 1400

x = 1400/200 = 7 months

He needs to save for 7 months.

7 0

2 years ago

Please helpppppppp -2p-4=2

OlgaM077 [116]

p = -3

Step-by-step explanation:

-2p-4=2

add 4 both sides

-2p-4+4=2+4

-2p=6

divide -2 both sides

-2p/-2=6/-2

p = -3

hope it's helpful ❤❤❤

THANK YOU.

5 0

2 years ago

At 10 am a 6-foot- tall man casts a 4.5 foot shadow. How long a shadow cast by a 50-foot tree?

vaieri [72.5K]

6 foot makes 4.5 foot shadow
1 foot makes=4.5/6
so 50 foot =4.5/6*50 = tree makes 37.5 foot shadow

4 0

2 years ago