HELP plsss if I don’t answer this I can’t go to lunch

If h(x)=(f o g) (x) and h(x)= ∛x+3, find g( x) if f(x)= ∛x+2 (picture attached)

Answer:

g(x) = x+1

Step-by-step explanation:

Informally, you can see that the function h(x) takes the root of a value that is 1 more than the value under the same radical in f(x). This suggests that adding 1 to x in f(x) will give you h(x). That is, ...

h(x) = f(x+1) = f(g(x))

so

g(x) = x+1

_____

More formally, you can apply the inverse of the function f(x) to the equation ...

h(x) = f(g(x))

f^-1(h(x)) = f^-1(f(g(x))) . . . inverse function applied

f^-1(h(x)) = g(x) . . . . . . . . . simplified

Now f^-1(x) can be found by solving for y in ...

x = f(y)

x = ∛(y+2) . . . . . . . . . definition of f(y)

x^3 = y+2 . . . . . . . . . cube both sides

x^3 -2 = y = f^-1(x) . . . subtract 2 from both sides

So, f^-1(h(x)) is ...

f^-1(h(x)) = g(x) = (∛(x+3))^3 -2 = x+3 -2

g(x) = x+1

5 0

3 years ago

Two cargo ships are sailing a direct course into harbor. Ship A is 22 miles from harbor. Ship Bis sailing into harbor on a cours

s344n2d4d5 [400]

Answer:

The distance of ship B from the Harbor is 32.26 miles

Step-by-step explanation:

Hello, great question. These types are questions are the beginning steps for learning more advanced Equations.

I have added a visual aid of the problem. As we can see the courses of both ship to the harbor forms a triangle with ship B being the hypotenuse. Since we are given the distance of the course for ship A and the angle between both ships, we can use this information with the <u>COSINE operator</u> to solve for the length of the course of ship B.

$cos(x) = \frac{adjacent}{hypotenuse}$

$cos(47) = \frac{22miles}{hypotenuse}$ .... flip both fractions.

$\frac{1}{cos(47)} = \frac{hypotenuse}{22miles}$ .... multiply both sides by 22

$\frac{22mi}{cos(47)} = hypotenuse$

$32.26mi = hypotenuse = B$

So the distance of ship B from the Harbor is 32.26 miles

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

3 0

3 years ago

An online furniture store sells chairs for $200 each and tables for $600 each. Every

Vladimir79 [104]

Answer:

Step-by-step explanation:

Answer:

If the minimum 13 chair were sold , then the minimum number of Table sold is 14

Step-by-step explanation:

Given as :

The cost of each chair = $ 200

The cost of each table = $ 600

The total number of furniture sold per day = 32

The minimum amount of selling per day = $ 12000

Let the total number of chair = C

The total number of table = T

So , according to question

C + T = 32 .......1

200 C + 600 T = 12000 .......2

Solving eq 1 and 2

200 C + 600 T = 12000

200 × ( C + T ) = 32 × 200

I.e 200 C + 200 T = 6400

or, ( 200 C + 600 T ) - ( 200 C + 200 T ) = 12,000 - 6400

Or, 400 T = 5600

∴ T =

I.e T = 14

Put The value of T in eq 2

So, 200 C + 600 × 14 = 12000

or , 200 C + 8400 = 12,000

Or, 200 C = 12000 - 8400

Or, 200 C = 3600

∴ C =

I.e C = 18

The number of chair sold is 18

If the number of chair sold is 13 ,

Then the min number of table sold = 200 × 18 + 600 T = 12000

i.e 600 T = 12000 - 3600

or, 600 T = 8400

∴ T =

I.e T = 14

Hence if the minimum 13 chair were sold , then the minimum number of Table sold is 14 . Answer

8 0

3 years ago

Write the standard form of the line that has a slope of - and y-intercept of -2. Include your work in your final answer. Type yo

ehidna [41]

You need to go from slope-intercept ( $y=mx+b$ ) to standard form ( $ax + by = c$ ).

slope-intercept form of your provided values:
$y=-x-2$
now, solve for x and y
$x+y=-2$

Your answer is $x+y=-2$ .

6 0

3 years ago

Read 2 more answers

Find two consecutive integers whose sum is 35

4vir4ik [10]

Two consecutive integers are 17+18

6 0

3 years ago