1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
seropon [69]
2 years ago
15

If(x) = x + 2 and h(x) = x-1, what is f • h](-3)?

Mathematics
1 answer:
deff fn [24]2 years ago
4 0

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.

You might be interested in
What is the slope to this line?
Artyom0805 [142]

Answer:

hello :

Hello : let  A(1,0)    B(0,2)  in this line

the slope is :   (YB - YA)/(XB -XA)




5 0
3 years ago
What is the expression below?<br> 26 + 67 + 3x2³
Alenkasestr [34]

Answer:

24x+93

That's the answer to the equation that was what you were asking for right?

5 0
3 years ago
In the given figure, ΔABC is a right triangle.
LUCKY_DIMON [66]

Answer:

its an isosceles triangle which means that the sides a and c are the same

so C is the correct answer!!

Step-by-step explanation:

8 0
1 year ago
Which of the following equations is equivalent to 4[x + 2(3x – 7)] = 22x – 65?
pickupchik [31]

Answer:

X= -3/2

Step-by-step explanation:

6x/6=-9/6

6 0
3 years ago
Solve issuing Pythagorean theorem
Anna35 [415]

Step-by-step explanation:

(8x8) + (16x16) = 64+256 = 320

√320 = 17.9

8 0
2 years ago
Other questions:
  • Describe a situation with two quantities that have a proportional linear relationship.
    7·1 answer
  • Please answer quickly! Will give 5 star and brainliest for quickest answer.
    9·1 answer
  • Can someone answer this?
    10·1 answer
  • Which represents the inverse of the function f(x) = 4x?
    13·1 answer
  • Find the value of x. Select one: a. 2.3 inches b. 3.3 inches c. 4.1 inches d. 6.1 inches
    11·1 answer
  • You can have a radical in the dominator for an answer true or false
    15·1 answer
  • Help please!!! Thanks
    7·1 answer
  • Trong tháng 05, tại cơ sở sản xuất có tài liệu sau. Tính thuế TTĐB mà cs phải nộp trong tháng. 1. Mua 5.000 lít rượu nguyên chất
    6·1 answer
  • Simplify using basic trigonometric identities
    11·1 answer
  • Using the identity sin? O + cos? O = 1, find the value of tan O, to the nearest
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!