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Tems11 [23]
3 years ago
13

State of the given functions are inverses

Mathematics
1 answer:
bonufazy [111]3 years ago
3 0

Answer:

1) They are not inverses

2) They are inverses

Step-by-step explanation:

We need to find the composition function between these functions to verify if these functions are inverses. If f[g(x)] and g[f(x)] are equal to x they are inverses.

<u>1)</u>

<u>Let's find f[g(x)] and simplify.</u>

f[g(x)]=\frac{1}{2}g(x)+\frac{3}{2}

f[g(x)]=\frac{1}{2}(4-\frac{3}{2}x)+\frac{3}{2}    

f[g(x)]=\frac{7}{2}-\frac{3}{4}x

As f[g(x)] is not equal to x, these functions are not inverses.

2)

<u>Let's find f[g(x)] and simplify.</u>

f[g(n)]=\frac{-16+(4n+16)}{4}

f[g(n)]=\frac{-16+4n+16}{4}

f[g(n)]=\frac{4n}{4}

f[g(n)]=n

Now, we need to find the other composition function g[f(x)]

<u>Let's find g[f(x)] and simplify.</u>

g[f(x)]=4(\frac{-16+n}{4})+16

g[f(x)]=-16+n+16

g[f(x)]=n

Therefore, as f[g(n)] = g[f(n)] = n, both functions are inverses.

I hope it helps you!  

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Choose the symbol that correctly compares the fractions below.<br> 8/9 ? 1/9
gladu [14]

Answer:

Which means that this equation is also true: 8/9 > 1/9

Step-by-step explanation:

Is 8/9 less than 1/9? Is 8/9 smaller than 1/9? These are the same questions with one answer.

To get the answer, we first convert each fraction into decimal numbers. We do this by dividing the numerator by the denominator for each fraction as illustrated below:

8/9 = 0.889

1/9 = 0.111

Then, we compare the two decimal numbers to get the answer.

0.889 is not less than 0.111.

Therefore, 8/9 is not less than 1/9 and the answer to the question "Is 8/9 less than 1/9?" is no.

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Answer:

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Step-by-step explanation:

Scale of 1:400,000

Each means that each centimeter on the map has the real distance of 400,000 cm = 4 km

What is the real-life distance between the park and the theatre?

On the map, the distance between them is of 3 centimeters.

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The real-life distance between the park and the theatre is of 12 km.

3 0
3 years ago
32% of 1600 = 512
yaroslaw [1]

Answer:

  • 64%: 1024
  • 96%: 1536
  • 132%: 2112
  • 232%: 3712

Step-by-step explanation:

<u>64% of 1600</u>

  64% of 1600 = 2 × (32% of 1600) = 2×512

  64% of 1600 = 1024

<u>96% of 1600</u>

  96% of 1600 = 3 × (32% of 1600) = 3×512

  96% of 1600 = 1536

<u>132% of 1600</u>

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  132% of 1600 = 2112

<u>232% of 1600</u>

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3 years ago
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The length of a rectangle is 2 meters more than its width. The area of the rectangle is 80 square meters. What is the length and
insens350 [35]

Answer:

Step-by-step explanation:

Formula

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Givens

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L = W + 2

Solution

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Area = (W+2)*W = 80            Remove the brackets.

Area = W^2 + 2W = 80         Subtract 80 from both sides.

Area = w^2+2W-80=80-80  Combine

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