f(x)=2x^2+2mx+12 If f(x-3) is even, what is the value of "m"?
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Do you mean f(x-3) is an even function?
Originally Posted by kastamonu f(x)=2x^2+2mx+12 If f(x-3) is even, what is the value of "m"? Did you consider just multiplying it out? f(x- 3)= 2x^2- 12x+ 9+ 2mx- 6m+ 12= 2x^2+(2m- 12)x+ 21- 6m. A polynomial function is even if and only if it has only even powers of x.
Originally Posted by Prove It Do you mean f(x-3) is an even function? Yes.
Originally Posted by HallsofIvy Did you consider just multiplying it out? f(x- 3)= 2x^2- 12x+ 9+ 2mx- 6m+ 12= 2x^2+(2m- 12)x+ 21- 6m. A polynomial function is even if and only if it has only even powers of x. Then (2m- 12)=0?
Eventually, you will have to think for yourself!
Originally Posted by HallsofIvy Did you consider just multiplying it out? f(x- 3)= 2x^2- 12x+ 9+ 2mx- 6m+ 12= 2x^2+(2m- 12)x+ 21- 6m. A polynomial function is even if and only if it has only even powers of x. That is not true. A function is even if for all x. Consider the function , then . The OP needs to check what f(x-3) is and then set it equal to f( -(x-3) ).
Originally Posted by Prove It That is not true. A function is even if for all x. Consider the function , then . Yes, and has x to an odd power. The OP needs to check what f(x-3) is and then set it equal to f( -(x-3) ). No, that would check if f is even. The OP needs to check if f(x- 3)= f(-x-3).
f(x- 3)= f(-x-3)? Why do I have to check in this way?
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