Question

A function is 1 when its argument is zero. Its value is 1/12 times as big as its slope at any point. What is the function

Answer 1

The function is
`f(x)=(1)/(12)x;x\\eq0` and
`f(x)=1;\ x=0`

Explanation:

The first thing to notice is that the domain of the function is divided in x=0 and x≠0. Then, when the value of x is 0, the value of f(x) is 1, which is clear in the question.

On the other hand, for all values of x but zero (this means x≠0), the function is defined as 1/12 of the slope, and the intercept is zero because it doesn't say anything about it.

Then, for x≠0, the function is defined as

`f(x)=(1)/(12)x;x\\eq0`