How many real solutions does $x^{4} + x^{2} + 1 = 0$ have?

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$f (x) = 2 x + 3$ and $g (x) = x^{2}$ . What is the sum of the solutions of $f (g (x)) = g (f (x))$ ?
$f (x) = \frac{x + 1}{x - 2}$ for $x \neq = 2$ . Which expression is $f^{- 1} (x)$ ?
The point $(3, 5)$ lies on the graph of $y = f (x)$ . Which point must lie on the graph of $y = f (2 x - 1)$ ?
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 $x^{2} + y^{2}$ ?
The circle $x^{2} + y^{2} = 25$ and the line $y = x + 1$ intersect at two points. What is the sum of the $y$ -coordinates of these points?