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3 years ago

Which statement could be used to explain why the function h(x) = x has an inverse relation that is also a function?

Mathematics

1 answer:

hodyreva [135]3 years ago

3 0

Answer:

Since h(x) is a one-to-one function, this means its inverse is also a function

Step-by-step explanation:

The key idea here is knowing that a function needs to be a 'many - to -one' operation (Many could also include one-to-one functions. The key if that for any x, there is only one f(x) value).

This means that for a function to have an inverse, it needs to be one-to-one. Since the domain and range switch when we look at inverse relations, and so if we have a many-to-one function, then it's inverse would be one-to-many. But we need it to be one-to-one. So the original function would need to be one-to-one.

However the short answer is to just know the 'theorem' which says that a function has an inverse function if and only if it is a one-to-one function.

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Answer:

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Step-by-step explanation:

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Answer:

$75\sqrt{2}(\sqrt{3}-1)$

Step-by-step explanation:

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3 years ago

Comparing the two ratios 2/4 and 1/2 2/4 is larger

kumpel [21]

Answer:

3.5 : 7 > 1.2 : 2.5.

Step-by-step explanation:

1. Compare the ratios 4 : 5 and 2 : 3.

Solution:

Express the given ratios as fraction

4 : 5 = 4/5 and 2 : 3 =2/3

Now find the L.C.M (least common multiple) of 5 and 3

The L.C.M (least common multiple) of 5 and 3 is 15.

Making the denominator of each fraction equal to 15, we have

4/5 = (4 ×3)/(5 ×3) = 12/15 and 2/3 = (2 ×5)/(3 ×5) = 10/15

Clearly, 12 > 10

Now, 12/15 > 10/15

Therefore, 4 : 5 > 2 : 3.

2. Compare the ratios 5 : 6 and 7 : 9.

Solution:

Express the given ratios as fraction

5 : 6 = 5/6 and 7 : 9 =7/9

Now find the L.C.M (least common multiple) of 6 and 9

The L.C.M (least common multiple) of 6 and 9 is 18.

Making the denominator of each fraction equal to 18, we have

5/6 = (5 ×3)/(6 ×3) = 15/18 and 7/9 = (7 ×2)/(9 ×2) = 14/18

Clearly, 15 > 14

Now, 15/18 > 14/18

Therefore, 5 : 6 > 7 : 9.

3. Compare the ratios 1.2 : 2.5 and 3.5 : 7.

Solution:

1.2 : 2.5 = 1.2/2.5 and 3.5 : 7 =3.5/7

1.2/2.5 = (1.2 ×10)/(2.5 ×10 ) = 12/25 and 3.5/7 = (3.5 ×10)/(7 ×10) = 35/70 = 1/2

[We removed the decimal point from the ratios now, we will compare the ratio]

Now find the L.C.M (least common multiple) of 25 and 2

The L.C.M (least common multiple) of 25 and 2 is 50.

Making the denominator of each fraction equal to 50, we have

= 12/25 = (12 ×2)/(25 ×2) = 24/50 and 1/2 = (1 ×25)/(2 ×25) = 25/50

Now, 25/50 > 24/50

Therefore, 3.5 : 7 > 1.2 : 2.5.

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3 years ago

Simplify this expression

antiseptic1488 [7]

Answer:

2/(3x-2)²

Step-by-step explanation:

4x²-6x³-2x²+6x³/4x²-6x³-6x³+9x^4=

2x²/4x²-12x³+9x^4=

2x²/x²(4-12x+9x²)=

2/9x²-12x+4

2/(3x-2)²

6 0

4 years ago

Which statement could be used to explain why the function h(x) = x has an inverse relation that is also a function?​

Which statement could be used to explain why the function h(x) = x has an inverse relation that is also a function?