注意：函数并不是数字

Consider the simple function $f(x) = x.$

What is $f(3)$ ?

When is $f(x) = 3$ ?

When is $f(x)=4$ ?

Is it okay here to say $f(x) = 3$ ?

As you see above, remember that functions are maps that take numbers as input and give numbers as output. While we may add them, divide them, and perform other arithmetic operations on them like we do with numbers, they are not numbers themselves.

Just as some practice. Consider the function $g(x) = 3$

When is $g(x) = 3$ ?

When we say here that $g(x) = 3,$ what is " $3$ "?

Check out Warning: Derivative of 3^2 for an example of this.

注意：函数并不是数字

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