Thread: Help: Definition of function

Greetings.

For a function, f(x), defined as follows:

1 if |x| < (1/2)
0 otherwise

how will the function f(-x) be defined?

Would greatly appreciate assistance.

Best regards,
wirefree

For a function, f(x), defined as follows:

1 if |x| < (1/2)
0 otherwise

how will the function f(-x) be defined?

1 if -.5 < -x < .5
0 otherwise

Seems like the only plausible answer to me.

Originally Posted by Isimbot

1 if -.5 < -x < .5
0 otherwise

Seems like the only plausible answer to me.

Appreciate the prompt response, Isimbot.

Your response implies:

f(x) = f(-x)

Is this true for all functions?

Look forward to your response.

Best regards,
wirefree

Originally Posted by wirefree

Greetings.

For a function, f(x), defined as follows:

1 if |x| < (1/2)
0 otherwise

how will the function f(-x) be defined?

since |x| = |-x| , the function will be the same.

Originally Posted by wirefree

Appreciate the prompt response, Isimbot.

Your response implies:

f(x) = f(-x)

Is this true for all functions?

Look forward to your response.

Best regards,
wirefree

With the stated definition, yes.

Originally Posted by wirefree

Appreciate the prompt response, Isimbot.

Your response implies:

f(x) = f(-x)

Is this true for all functions?

Look forward to your response.

Best regards,
wirefree

No, of course not. It is true for all "even" functions- in fact, that is precisely the definition of "even function". And the function you gave is an even function.

|x|, by definition, is even.

Appreciate the help.

Best regards,
wirefree