Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2016年7月11日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2016年12月24日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2016年11月2日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2021年6月29日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2013年5月30日 · Below I show how the standard proof (e.g. egreg's answer) is a special case of more general results on uniqueness theorems and Wronskians.

2017年12月16日 · A function property holding at a single point or at all points are two very different issues. The derivative of a function requires the knowledge of infinitely many values within a neighborhhood of the point (it takes the computation of a limit).

2017年6月18日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

$$\text {Applying the definition: }\ f(0)=-f(0) ,$$ $$\text {so if}\ f(0) =c≠0 \text{ you would have two different values in x=0, c and -c}$$ $$\text {which is clearly impossible, so you must have }\ f(0)=0$$ $$\text{because for every x in the domain you must have only one f(x)}$$ $$\text{and 0 is the only value that satisfy that relation.}$$

How do you solve questions like f(0)=2, f(2)=4 and write an equation for the linear function? That's the same problem as Find the equation of the line that passes through the two points (0,2) and (2,4) except that when you finish you write f(x) instead of y.