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finlep [7]
3 years ago
9

I would really appreciate if any body could help if not it’s okay

Mathematics
1 answer:
Archy [21]3 years ago
6 0
What do you need help with
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If(x) = x + 2 and h(x) = x-1, what is f • h](-3)?
deff fn [24]

Answer/Step-by-step explanation:

Composition functions are functions that combine to make a new function. We use the notation ◦ to denote a composition.

f ◦ g is the composition function that has f composed with g. Be aware though, f ◦ g is not

the same as g ◦ f. (This means that composition is not commutative).

f ◦ g ◦ h is the composition that composes f with g with h.

Since when we combine functions in composition to make a new function, sometimes we

define a function to be the composition of two smaller function. For instance,

h = f ◦ g (1)

h is the function that is made from f composed with g.

For regular functions such as, say:

f(x) = 3x

2 + 2x + 1 (2)

What do we end up doing with this function? All we do is plug in various values of x into

the function because that’s what the function accepts as inputs. So we would have different

outputs for each input:

f(−2) = 3(−2)2 + 2(−2) + 1 = 12 − 4 + 1 = 9 (3)

f(0) = 3(0)2 + 2(0) + 1 = 1 (4)

f(2) = 3(2)2 + 2(2) + 1 = 12 + 4 + 1 = 17 (5)

When composing functions we do the same thing but instead of plugging in numbers we are

plugging in whole functions. For example let’s look at the following problems below:

Examples

• Find (f ◦ g)(x) for f and g below.

f(x) = 3x + 4 (6)

g(x) = x

2 +

1

x

(7)

When composing functions we always read from right to left. So, first, we will plug x

into g (which is already done) and then g into f. What this means, is that wherever we

see an x in f we will plug in g. That is, g acts as our new variable and we have f(g(x)).

g(x) = x

2 +

1

x

(8)

f(x) = 3x + 4 (9)

f( ) = 3( ) + 4 (10)

f(g(x)) = 3(g(x)) + 4 (11)

f(x

2 +

1

x

) = 3(x

2 +

1

x

) + 4 (12)

f(x

2 +

1

x

) = 3x

2 +

3

x

+ 4 (13)

Thus, (f ◦ g)(x) = f(g(x)) = 3x

2 +

3

x + 4.

Let’s try one more composition but this time with 3 functions. It’ll be exactly the same but

with one extra step.

• Find (f ◦ g ◦ h)(x) given f, g, and h below.

f(x) = 2x (14)

g(x) = x

2 + 2x (15)

h(x) = 2x (16)

(17)

We wish to find f(g(h(x))). We will first find g(h(x)).

h(x) = 2x (18)

g( ) = ( )2 + 2( ) (19)

g(h(x)) = (h(x))2 + 2(h(x)) (20)

g(2x) = (2x)

2 + 2(2x) (21)

g(2x) = 4x

2 + 4x (22)

Thus g(h(x)) = 4x

2 + 4x. We now wish to find f(g(h(x))).

g(h(x)) = 4x

2 + 4x (23)

f( ) = 2( ) (24)

f(g(h(x))) = 2(g(h(x))) (25)

f(4x

2 + 4x) = 2(4x

2 + 4x) (26)

f(4x

2 + 4x) = 8x

2 + 8x (27)

(28)

Thus (f ◦ g ◦ h)(x) = f(g(h(x))) = 8x

2 + 8x.

4 0
2 years ago
A certain ferry moves up and down a river between Town A and
Blizzard [7]

Answer: 60 miles

Step-by-step explanation:

Given

It takes ferry 2 hours to travel to town A and only 1.5\ hr to travel back to town B.

Speed of current is u=5\ mph

Suppose the speed of the ferry is v mph

Distance traveled in both the cases is same, but it took more time traveling to city A that is, ferry is moving upstream and downstream for returning time.

\Rightarrow 2(v-5)=1.5(v+5)\\\Rightarrow 2v-10=1.5v+7.5\\\Rightarrow 0.5v=17.5\\\Rightarrow v=35\ mph

Distance between the towns is 2\times (35-5)=60\ \text{miles}

5 0
2 years ago
Read 2 more answers
Lacie wants to paint her bedroom walls. She gas to cover 1,165.5 square feet. About how many gallons of paint will she need? Gal
DanielleElmas [232]

Answer:

1. 4.66 gallons 2. 2.33 gallons 3. 1.55 gallons

Step-by-step explanation:

1. If her gallons cover is 250 square feet, the number of gallons of paint Lacie would need to cover 1,165.5 square feet of bedroom walls is

1,165.5/250 = 4.66 gallons

2. If her gallons cover is 500 square feet, the number of gallons of paint Lacie would need to cover 1,165.5 square feet of bedroom walls is

1,165.5/500 = 2.33 gallons

3. If her gallons cover is 750 square feet, the number of gallons of paint Lacie would need to cover 1,165.5 square feet of bedroom walls is

1,165.5/750 = 1.55 gallons

4 0
3 years ago
4(3d-2x)-(2d-5x)<br> Maths help plz.....
nata0808 [166]

Answer:

10d - 3x

Step-by-step explanation:

Distribute the 4: 12d - 8x

Distribute the -1: -2d + 5x

Add like terms: 10d - 3x

6 0
3 years ago
The cost for a pack of 24 pens is $4.08 . Find the unit price in dollars per pen. If necessary, round your answer to the nearest
Eduardwww [97]

Answer:

The unit price is 0.17 cents per pen.

4 0
3 years ago
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