# Which of the following is/are true?

• Jaco Viljoen
In summary: My apologies for the confusion. In summary, the statements that are true are B) and C). In statement A), f(x) multiplied by f(-x) is equal to 1. In statement C), the answer for h(2) is 2, not ±2.
Jaco Viljoen

## Homework Statement

Which of the following statements are true?
A)
If f(x)=ex, then f(x)⋅f(-x)=1

B)
If g(x)=1/x, then g (1/x)=x

C)
If h(x)=√(x+2), then h(2)=±2

## The Attempt at a Solution

Only B

Jaco Viljoen said:

## Homework Statement

Which of the following statements are true?
A)
If f(x)=ex, then f(x)⋅f(-x)=1

B)
If g(x)=1/x, then g (1/x)=x

C)
If h(x)=√(x+2), then h(2)=±2

## The Attempt at a Solution

Only B
I agree, but why do you think that A and C are not true?

Jaco Viljoen
A) doesn't seem to make sense to me... although x is still unknown.
C)The answer would be 2 not ±2.

Jaco Viljoen said:
A) doesn't seem to make sense to me... although x is still unknown.
But even without having a specific value for x, can't you evaluate f(x) - f(-x), to see whether it comes out to 1? Otherwise your answer is nothing more than a guess.
Jaco Viljoen said:
C)The answer would be 2 not ±2.
Yes.

If f(x)=ex, then f(x)⋅f(-x)=1 Not true:
-ex

Jaco Viljoen said:

## Homework Statement

Which of the following statements are true?
A)
If f(x)=ex, then f(x)⋅f(-x)=1

B)
If g(x)=1/x, then g (1/x)=x

C)
If h(x)=√(x+2), then h(2)=±2

## The Attempt at a Solution

Only B

In (A), it looks to me as though you are writing (i): ##f(x) \times f(-x)##, while Mark44 seems to see (ii): ##f(x) - f(-x)##. Which do you mean: (i) or (ii)?

Jaco Viljoen
Oops! My mistake! Thanks for pointing out my error, Ray. I misread that dot as a minus sign. f(x) X f(-x) is indeed equal to 1.

Jaco Viljoen

## 1. What is the purpose of asking "Which of the following is/are true?"

The purpose of this question is to assess the validity and accuracy of a statement or group of statements. It prompts the person to analyze the information and determine which option is correct.

## 2. How can I determine which of the following is/are true?

The best way to determine the truthfulness of a statement is to gather evidence and conduct experiments to test its validity. It is important to use reliable sources and critical thinking skills when evaluating information.

## 3. Are all of the options in "Which of the following is/are true?" always mutually exclusive?

No, it is possible for multiple options to be true. This is why it is important to carefully evaluate each statement and consider all possible scenarios.

## 4. Can I trust the accuracy of the options presented in "Which of the following is/are true?"

It depends on the source and reliability of the information. It is important to use credible sources and verify information before accepting it as true.

## 5. How can I improve my critical thinking skills when evaluating "Which of the following is/are true?"

Some ways to improve critical thinking skills include practicing logical reasoning, evaluating different perspectives, and questioning assumptions. It can also be helpful to seek out diverse sources of information and actively engage in discussions with others.

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