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Korolek [52]
3 years ago
9

How to do composition of functions​

Mathematics
1 answer:
KengaRu [80]3 years ago
5 0
<h2><u><em>If you rather have the link to get this info lmk!!</em></u></h2>

Example: f(x) = 2x+3 and g(x) = x2

"x" is just a placeholder. To avoid confusion let's just call it "input":

f(input) = 2(input)+3

g(input) = (input)2

Let's start:

(g º f)(x) = g(f(x))

First we apply f, then apply g to that result:

Function Composition - (g º f)(x) = (2x+3)2

What if we reverse the order of f and g?

(f º g)(x) = f(g(x))

First we apply g, then apply f to that result:

Function Composition - (f º g)(x) = 2x2+3

We get a different result!  When we reverse the order the result is rarely the same.  So be careful which function comes first.

<h2 />
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Brenda and her best friend went on a vacation together. They both paid for a flight, and Brenda had a fancy room for $150 per ni
Mila [183]

Answer:

A. 2x + 150y = 1,500

   2x + 120y = 1,320

The flights were $300 each, and they stayed 6 nights.

B. $1,380

Step-by-step explanation:

Let x be the cost of the flight (in one side) and y be the number of nights on their vacation.

A. Brenda had a fancy room for $150 per night, then she paid $150y for y nights.  Brenda's total is $1,500, then

150y+2x=1,500

Brenda's friend had a smaller room for $120 per night, then she paid $120y for y nights.  Brenda's friend total is $1,320, then

120y+2x=1,320

Subtract two equations:

150y+2x-120y-2x=1,500-1,320\\ \\30y=180\\ \\y=6

Substitute into the first equation:

150\cdot 6+2x=1,500\\ \\900+2x=1,500\\ \\2x=600\\ \\x=300

Hence

2x + 150y = 1,500

2x + 120y = 1,320

The flights were $300 each, and they stayed 6 nights.

B. If a third friend joined them and stayed in a mid-range room for $130 per night, then he paid \$130\cdot 6=\$780

The total cost is

\$780+\$600=\$1,380

7 0
4 years ago
FREE BRAINLIEST. PLEASE ANSWER STEPBY STEP 1. 2. 3.
Flura [38]

Answer:

8

Step-by-step explanation:

First do whats in the parenthesis:

(8+18/9)

Using PEMDAS again, we do the division first:

(8+2)

Now addition:

(10)

Now subtraction:

(10)-2

8

3 0
3 years ago
Cassie has 1/2 pound of sugar in her cabinet. Her cake calls for 2/10 of a pound of sugar. How many cakes can she make?
dmitriy555 [2]
1/2 is also 5/10 so she can make 2 cakes, but really its 2 and a half cakes but u cant make a half
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4 years ago
PLEASE HELP ME ASAP :)))))))))
Scorpion4ik [409]

Answer:

(1) x= −1 /2 y+ 5 /2

(2) x= −1 /2 y−2

Step-by-step explanation:

<u>(1)</u> 2x+y=5

Step 1: Add -y to both sides.

2x+y+−y=5+−y

2x=−y+5

Step 2: Divide both sides by 2.

2x /2 = (−y+5)/2  

x= −1 /2 y+ 5 /2

<u>(2) </u>Step 1: Flip the equation.

−2x−4=y

Step 2: Add 4 to both sides.

−2x−4+4=y+4

−2x=y+4

Step 3: Divide both sides by -2.

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3 years ago
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Answer:

-x^2 - 20x -4 = 0

Step-by-step explanation:

I assume you meant (x-8)(2x+3) = (3x-5)(x+4).

Perform the two indicated multiplications and then combine like terms:

2x^2 + 3x - 16x - 24 = 3x^2 + 12x - 5x - 20

Combine the x terms on each side:

2x^2 - 13x - 24 = 3x^2 + 7x - 20

Subtract 3x^2 from both sides:

-x^2 - 13x - 24 = 7x - 20

Subtract 7x from both sides:

-x^2 - 20x - 24 = -20

Add 20 to both sides:

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