Concept and equation of a function

To calculate the images of $-2$ and $1$ it is enough to substitute in the function:

$$f (-2) = 2 \cdot (-2) +1 =-4 + 1 =-3 $$

$$f (1) = 2 \cdot 1 +1 = 2 + 1 = 3 $$

To calculate the antiimage at point $1$, that is to say $f^{-1}(1)$, we must equal the expression of the function to the number of the antiimage that we want to calculate, and solve the resultant equation:

$$f^{-1}(1): \ 1= 2x + 1$$

$$2x = 1 - 1 = 0$$

$$x = 0$$

Therefore, $f^{-1}(1)=0$