Function's Fun f(x^2−2016x)=f(x)⋅x+2016

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In summary, the domain of the function is all real numbers except for 2016, as it would result in division by zero. The function is not one-to-one and can result in the same output for different inputs. The range of the function is all real numbers and it is undefined at x = 2016. The function can be rewritten as f(x) = x^2-2016x.
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f(x^2*2016x) = f(x)x+2016
Then f(2017) = ?
 
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  • #2
Isn't "x^2*2016x" the same as "2016x^3"?
 
  • #4
Thanks, skeeter. That sounds more reasonable.

f(x^2- 2016x)= f(2017) if x^2- 2016x= 2017. That is the same as x^2- 2016x- 2017= (x+ 1)(x- 2017)= 0 so either x= -1 or x= 2017.

So either f(2017)= -1(f(-1))+ 2016 or f(2017)= 2017 f(2017)+ 2016.

For the latter, -2016= 2016 f(2017) so f(2017)= -1.
 

1. What is the domain of the function?

The domain of the function is all real numbers except for 2016, since the expression x^2-2016x would result in division by zero.

2. Is the function one-to-one?

No, the function is not one-to-one because for two different inputs, x and y, the function can result in the same output f(x) = f(y) if x^2-2016x = y^2-2016y.

3. What is the range of the function?

The range of the function is all real numbers, as the function can take on any value depending on the input x.

4. Is there a specific value for which the function is undefined?

Yes, the function is undefined at x = 2016, as mentioned in the domain.

5. Can this function be simplified or rewritten?

Yes, this function can be rewritten as f(x) = x^2-2016x, since f(x) is equal to both sides of the original equation.

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