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State whether the following statement is true or false:

and are inverses of one another.

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True

False

answer is A.

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Detailed Solution

The given statement is true.
Concept- Prior to comparing it to the second number, we shall first determine the first number's reciprocal. We can conclude that the statement is accurate if they are the same.

is the first number that is given to us.
Since, a number's reciprocal,

.
The result is

.
By applying this idea and taking

, we get:
The reciprocal of

equals

.
Given that Question Image

,
Thus, we obtain: Question Image

.
Because

, we know that multiplying a number by one has no effect on its value.
So,

It can be rewritten as follows:

.
Because we are aware that

for all a, this is done.
According to this, Question Image

We are aware that square and square roots cancel one another. Thus, we obtain:

.
It is immediately obvious that this equals the second number provided to us.
So, the assertion is accurate.
Hence, the given statement is true.

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