# Math Help - Help: Definition of function

1. ## 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

2. 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.

3. Originally Posted by Isimbot
1 if -.5 < -x < .5
0 otherwise

Seems like the only plausible answer to me.
Appreciate the prompt response, Isimbot.

f(x) = f(-x)

Is this true for all functions?

Best regards,
wirefree

4. 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.

5. Originally Posted by wirefree
Appreciate the prompt response, Isimbot.

f(x) = f(-x)

Is this true for all functions?

Best regards,
wirefree
With the stated definition, yes.

6. Originally Posted by wirefree
Appreciate the prompt response, Isimbot.

f(x) = f(-x)

Is this true for all functions?