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
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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
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