What is the largest value of $\frac{1}{x ^{2} - 4 x + 7}$ for real $x$ ?

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$f (x) = 2 x + 3$ and $g (x) = x^{2}$ . What is the sum of the solutions of $f (g (x)) = g (f (x))$ ?
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The function $f$ is defined by $f (x) = x^{2} - 4 x + 7$ for $x \geq 2$ . What is the range of $f$ ?
If $x + y = 5$ and $x y = 6$ , what is the value of $x^{2} + y^{2}$ ?
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