Let $f(x) = 5x^2 - 4x + 2$ with its natural or implied domain.
Let $g(t) = \frac {3}{6-t}$ with its natural or implied domain.

$$(f \circ g)(y) = f(g(y)) = 5 \left ( \answer {\frac {3}{6-y}} \right )^2 - 4 \left ( \answer {\frac {3}{6-y}} \right ) + 2$$

$$(g \circ f)(w) = g(f(w)) = \frac {3}{6 - \left ( \answer {5w^2 - 4w + 2} \right )}$$

Let $f(x) = 3x^2 - x + 5$ with its natural or implied domain.
Let $g(t) = \frac {4}{7-t}$ with its natural or implied domain.

Thinking about $(g \circ f)(w) = g(f(w))$...

There are two numbers where $f(x) = 7$. One of them is $1$, the other is $\answer {\frac {-2}{3}}$.

$$(g \circ f)(w) = g(f(w)) = \frac {4}{7 - (5w^2 - 4w + 2)}$$

In the $g \circ f$ composition, $f$ is no longer allowed to equal $\answer {7}$.

Select all real numbers which cannot be in the domain of $g \circ f$.