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4 years ago

ALGEBRA 2!!!!!!!!! SHOW YOUR WORK!!!!!!!!!!!!! Do f(g(x)) and g(f(x))

Mathematics

1 answer:

bezimeni [28]4 years ago

4 0

$\bf f(x)=\cfrac{2x-3}{x+1}~\hspace{10em}g(x)=\cfrac{x+3}{2-x}
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
f(~~g(x)~~)\implies \cfrac{2[g(x)]-3}{[g(x)]+1}\implies \cfrac{2\left( \frac{x+3}{2-x} \right)-3}{\left( \frac{x+3}{2-x} \right)+1}\implies
\cfrac{\frac{2x+6}{2-x}-3}{\frac{x+3}{2-x}+1}
\\\\\\
\cfrac{\frac{2x+6-6+3x}{2-x}}{\frac{x+3+2-x}{2-x}}\implies \cfrac{2x+6-6+3x}{2-x}\cdot \cfrac{2-x}{x+3+2-x}\implies \cfrac{5x}{5}\implies x$

$\bf \rule{34em}{0.25pt}\\\\
g(~~f(x)~~)\implies \cfrac{[f(x)]+3}{2-[f(x)]}\implies \cfrac{\frac{2x-3}{x+1}+3}{2-\frac{2x-3}{x+1}}\implies \cfrac{\frac{2x-3+3x+3}{x+1}}{\frac{2x+2-(2x-3)}{x+1}}
\\\\\\
\cfrac{2x-3+3x+3}{x+1}\cdot \cfrac{x+1}{2x+2-(2x-3)}\implies \cfrac{2x-3+3x+3}{x+1}\cdot \cfrac{x+1}{2x+2-2x+3}
\\\\\\
\cfrac{5x}{5}\implies x$

and in case you recall your inverses, when f( g(x) ) = x, or g( f(x) ) = x, simply means, they're inverse of each other.

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Y is inversely proportional to (x+2)² when x=1, y=2

REY [17]

Answer:

y = 18 / (x + 2)²

Step-by-step explanation:

Inversely proportional

y * (x + 2)² = k

when x=1, y=2

k = 2 * (1 + 2)²

k = 18

-----------------------

y * (x + 2)² = 18

Divide both sides by (x + 2)²

y = 18 / (x + 2)²

6 0

3 years ago

Reuben made 4 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all 4 necklaces

zysi [14]

Answer:

$3.90

Step-by-step explanation:

The total cost was $24.40.

We know the cost for beads for each necklace is also $2.20, multiply this by four to find the cost of the beads for all the necklaces.

$2.20 × 4 = $8.80

Now we will subtract this from the total price.

$24.40 - $8.80 = $15.60

$15.60 Is the remaining cost for the pendants of all four necklaces. We will now divide this by four to find the price of a single pendant.

$15.60 ÷ 4 = $3.90

<u>This means the cost of each pendant is $3.90</u>

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3 years ago

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Your social media ad costs $2.50 per thousand impressions. You get 3.14 million impressions. What is your approximate bill?

melomori [17]

Answer:

7,850

Step-by-step explanation:

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3 years ago

Which of the following statements are true? Select all that apply.

Tom [10]

Answer: The statements in options 2 and 4 are true.

Explanation:

The LCM of two numbers is the smallest number that is multiple of both numbers.

The factor of 8 and 12 are,

$8=2\times 2\times 2$

$12=2\times 2\times 3$

Since 2 and 2 are common in both but 2 and 3 are not same, therefore the L.C.M. of 8 and 12 is,

$L.C.M.(8,12)=2\times 2\times 2\times 3=24$

Therefore the statement in option 1 is incorrect.

The factor of 6 and 9 are,

$6=2\times 3$

$9=3\times 3$

Since 3 is common in both but 2 and 3 are not same, therefore the L.C.M. of 6 and 9 is,

$L.C.M.(6,9)=2\times 3\times 3=18$

Therefore the statement in option 2 is correct.

The factor of 11 and 4 are,

$11=1\times 11$

$4=2\times 2$

Since all factor are different, therefore the L.C.M. of 11 and 4 is,

$L.C.M.(11,4)=1\times 11\times 2\times 2=44$

Therefore the statement in option 3 is incorrect.

The factor of 9 and 10 are,

$9=1\times 9$

$10=2\times 5$

Since all factor are different, therefore the L.C.M. of 9 and 10 is,

$L.C.M.(9,10)=1\times 9\times 2\times 5=90$

Therefore the statement in option 4 is correct.

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3 years ago

Anyone answer please it is my H.W <br>don't spam ❌❌

Nata [24]

Answer:

2a) = soln

20/3

2) divide the numeral by dinominator..

3)a) soln 7 3/4

4*7+3

= 31

do all like this ❣️

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2 years ago

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