Question

For the constant function v(x) = 1, which statement describes the additive and multiplicative inverses? Both inverses are equal to v(x). Neither inverse is equal to v(x). The additive inverse is equal to v(x), but the multiplicative inverse is not. The multiplicative inverse is equal to v(x), but the additive inverse is not.

Answer 1

Answer:

The multiplicative inverse is equal to v(x), but the additive inverse is not.

Step-by-step explanation:

Answer 2

The multiplicative inverse is equals to v(x) but the additive inverse is not.

What is additive inverse?

Additive inverse is a number which on getting added to the original number results in zero.

For example, 5 - 5 = 0

⇒ -5 is the additive inverse of 5.

What is multiplicative inverse?

Multiplicative inverse of a number is a value which when multiplied by the original number results in 1.

For example

$5 (\frac{1}{5} )= 1$

⇒ $\frac{1}{5}$ is the multiplicative inverse of 5.

According to the given question.

We have a function

v(x) = 1

Let the additive inverse of 1 is x.

⇒ 1 + x = 0

⇒ x = -1.

Hence, the additive inverse of 1 is -1.

Let the multiplicative inverse of 1 is y.

⇒ 1 × y = 1

⇒ y = 1/1

⇒ y = 1

Hence, the multiplicative inverse of 1 is 1.

From the above calculation we can see that, the multiplicative inverse is equals to v(x) but the additive inverse is not.

Thus last option is correct.

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