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Dominik [7]
4 years ago
13

How does national glory increase?​

Mathematics
1 answer:
posledela4 years ago
3 0
It generates the feeling of patriotism and respect towards the nation. It also makes people responsible and answerable to the nation.
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Which of the following have the property that a(x)=a−1(x)? I. y=x II. y=1/x III.y=x^2 IV. y=x^3 A. I and II, only B. IV, only C.
valentina_108 [34]

Answer:

<em>Correct answer:</em>

<em>A. I and II</em>

<em></em>

Step-by-step explanation:

First of all, let us have a look at the steps of finding inverse of a function.

1. Replace y with x and x with y.

2. Solve for y.

3. Replace y with f^{-1}(x)

Given that:

I.\ y=x \\II.\ y=\dfrac{1}x \\III.\ y=x^2 \\IV.\ y=x^3

Now, let us find inverse of each option one by one.

I. y = x, a(x) = x

Replacing y with and x with y:

x = y

x = a^{-1}(x) = a(x)  Hence, I is true.

II. y =\dfrac{1}{x}

Replacing y with and x with y:

x =\dfrac{1}{y}

x=\dfrac{1}{a^{-1}(x)}

\Rightarrow a^{-1}(x) = \dfrac{1}{x}

a^{-1}(x) = a(x)  Hence, II is true.

III. y =x^{2}

Replacing y with and x with y:

x =y^{2}\\\Rightarrow y = \sqrt x\\\Rightarrow a^{-1}(x) = \sqrt{x} \ne a(x)

 Hence, III is not true.

IV. y =x^{3}

Replacing y with and x with y:

x =y^{3}\\\Rightarrow y = \sqrt[3] x\\\Rightarrow a^{-1}(x) = \sqrt[3]{x} \ne a(x)

Hence, IV is not true.

<em>Correct answer:</em>

<em>A. I and II</em>

<em></em>

4 0
3 years ago
Kona’s mother realized that her age is the difference of Kona’s age squared and four. If k represents Kona’s age, which expressi
solmaris [256]

Answer:

k squared minus 4/ A

Step-by-step explanation:

took the test

4 0
3 years ago
Read 2 more answers
Find the x-intercept and the y-intercept of 2x + 6y =24
viktelen [127]

Answer:

x-intercept = 12, y-intercept = 4

Step-by-step explanation:

To find the x and y intercept, substitute 0 in for both values.

<u>Substitute 0 into x:</u>

2(0) + 6y = 24

6y = 24

<u>Divide each side by 6:</u>

y = 4

<u>Substitute 0 into y:</u>

2x + 6(0) = 24

2x = 24

<u>Divide each side by 2:</u>

x = 12

4 0
2 years ago
If 29 cos 0=21 find the value of 1/sin0-tan0..
Fantom [35]
It should be 21 20. Sorry if I got it wrong
7 0
3 years ago
Read 2 more answers
86% percent of senators support a bill. What fraction of senators support the bill?
Natali5045456 [20]

Answer:

\frac{43}{50}

Step-by-step explanation:

It was give that 86% percent of senators support a bill.

We want to determine the fraction of senators that supports the bill.

We just have to convert 86% into a fraction in its simplest form.

86\%=\frac{86}{100}

\frac{86}{100}=\frac{2\times43}{2\times50}

We cancel the common factors to obtain the fraction in the simplest form as:

\frac{43}{50}

7 0
3 years ago
Read 2 more answers
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