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Firdavs [7]
3 years ago
11

For f(x)= x+5 and g(x)=4x+2 find (fog)(x) And (gof)(x)

Mathematics
1 answer:
Svetllana [295]3 years ago
7 0

Composing functions means that the input of the outer functions is the output of the inner function.

In fact, you can rewrite the circle notation as

(f\circ g)(x)=f(g(x)),\quad (g\circ f)(x)=g(f(x))

So, we can substitute g(x) with its expression:

(f\circ g)(x)=f(g(x))=f(4x+2)

And since f(x)=x+5, we simply have to add 5 to its input:

f(4x+2)=(4x+2)+5=4x+7

Similarly, we have, substituting f with its expression,

(g\circ f)(x)=g(f(x))=g(x+5)

And since g(x)=4x+2, we have to multiply the input by 4 and add 2:

g(x+5)=4(x+5)+2=4x+20+2=4x+22

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Answer:

<h3>#1</h3>

<u>Trapezoid</u>

  • A = (b₁ + b₂)h/2
  • A = (4.8 yd + 29.4 ft)(8 yd)/2 = (14.6 yd)(4 yd) = 58.4 yd²
<h3>#2</h3>

<u>Rectangle</u>

  • A = ab
  • A = 2 yd * 3.1 yd = 6.2 yd²
<h3>#3</h3>

<u>Equilateral triangle</u>

  • A = √3/4a²
  • A = √3/4(10²) = 25√3
<h3>#4</h3>

<u>Regular octagon</u>

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6 0
3 years ago
Mrs. Barnes cuts1/2 of a piece of construction paper. She uses 1/6
denpristay [2]

Answer:

Step-by-step explanation:

what fraction?? she uses 1/6 of the construction paper

if you are referring to how much paper is left, its 2/6 aka 1/3

4 0
2 years ago
Read 2 more answers
The base area of a triangular pyramid is 22 square yards and the height of the pyramid is 15 yards. What is the volume of the tr
galben [10]

Answer:

110 yards^3

Step-by-step explanation:

volume of a  triangular pyramid=  1/3 area x height

1/3 x (22) x 15 = 110 yd^3

7 0
3 years ago
Systems of linear equations iready quiz
saw5 [17]

Answer:

<h2>One solution.</h2>

Step-by-step explanation:

The given question is

<em>Does the following system have One Solution, No Solution, or Infinite Solutions.   </em>

<em />y = 4x + 8\\y = -5x + 3<em />

<em />

<em />

To solve this system, we just need to multiply the first equation by -1, and then sum those equations.

-y = -4x - 8\\y = -5x + 3

0=-9x-5\\5=-9x\\x=-\frac{5}{9}

Then, we use this value to find the other one

y=4x+8\\y=4(-\frac{5}{9} )+8\\y=-\frac{20}{9}+8\\y =\frac{-20+72}{9} \\y=\frac{52}{9}

As you can observe, the system of equations have a unique solution.

Therefore, the answer is one solution.

7 0
3 years ago
Which best describes the transformation that occurs from
Law Incorporation [45]

Answer:

right 2 , up 3.

Step-by-step explanation:

The -2 moves 2 to the right and the + 3 means 3 up.

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