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2 problems match “range of a function”. Clear

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1. Distinct values of f(x) minus x ●○○○○ 10 ptsSuppose 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 $g(x)$?
2. Value missing from range of a Möbius function ●●●○○ 50 ptsThe function $f$ is defined by $f(x)= \frac{ax+b}{cx+d}$, where $a$, $b$, $c$ and $d$ are nonzero real numbers. It has the properties $f(19)=19$, $f(97)=97$ and $f(f(x))=x$ for all $x$ except $-\frac{d}{c}$. Find the unique number that is not in the range of $f$.