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2 problems match “inverse functions”. Clear

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1. 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 $f$.
2. Parameter sum for a symmetric rational function ●●●○○ 50 ptsGiven the function $f(x)=\frac{x}{ax+b}$ with $a\neq 0$, its graph passes through the point $(-4,4)$ and is symmetric about the line $y=-x$. Find the value of $a+b$. Give your answer as a decimal.