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ollegr [7]
3 years ago
14

I need help on number 3

Mathematics
1 answer:
melisa1 [442]3 years ago
3 0
3 by 21 because 1/4 of 12 is is 3
You might be interested in
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
Which of the following is the graph of y=3 sec [ 2(x-pi/2)] + 2
asambeis [7]

Answer:

A.) The first graph

Step-by-step explanation:

3 0
3 years ago
Two linear equations are shown. A coordinate grid with 2 lines. The first line is labeled y equals StartFraction one-third EndFr
Lorico [155]

Answer:

(7,\frac{13}{3})

Step-by-step explanation:

we have

<em>The equation of the first line</em>

y=\frac{1}{3}x+2 ------> equation A

<em>The equation of the second line</em>

y=\frac{4}{3}x-5 ------> equation B

Solve the system of equations by elimination

Multiply equation A by -4 both sides

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

-4y=-\frac{4}{3}x-8 --------> equation C

Adds equation B and equation C

y=\frac{4}{3}x-5\\-4y=-\frac{4}{3}x-8\\--------\\y-4y=-5-8\\-3y=-13\\y=\frac{13}{3}

<em>Find the value of x</em>

substitute the value of y

\frac{13}{3}=\frac{1}{3}x+2

\frac{1}{3}x=\frac{13}{3}-2

Multiply by 3 both sides

x=13-6

x=7

therefore

The solution to the system of equations is the point (7,\frac{13}{3})

5 0
3 years ago
Read 2 more answers
Please help and hurry!
Art [367]
A is the best answer…

Work:

-10x-(-4y) will equal -10x+4y the minus minus will cancel out

Please like and brainiest
6 0
2 years ago
Read 2 more answers
Mary borrowed $6000 from a bank for 3 years and was charged simple interest. The total interest that she paid on the loan was $7
daser333 [38]
4.17




Step by step : I don’t know if it’s right but I did $6000 x 3 cause he did it for 3 year and then it came up to $18,000 then I did what is the percentage of 750$ in $18,000 and got 4.17
3 0
3 years ago
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