Combinatorics › Sets and Venn diagrams › Counting relations and functions

Distinct values of f(x) minus x

High school · ●○○○○ 10 pts

Suppose the function

f(x)

is defined explicitly by the table

\begin{array}{c || c | c | c | c | c} x & 0 & 1 & 2 & 3 & 4 \\ \hline f(x) & 0 & 0 & 1 & 3 & 6 \end{array}

This function is defined only for the values of

x

listed in the table. Suppose

g(x)

is defined as

f(x)-x

for all numbers

x

in the domain of

f

. How many distinct numbers are in the range of

g(x)

?

range of a function counting distinct values