Page 24 of Introduction to Statistical Learning states:
...linear regression is a relatively inflexible approach, because it can only generate linear functions such as the lines shown in Figure 2.1 or the plane shown in Figure 2.3.
Later on, linear regression is defined more formally as assuming $f$ takes on form
$$ f(X) = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \ldots + \beta_p X_p $$
and "solving" for the $\beta_i$ using techniques like the "ordinary least squares" method (here I'm using the notation from the book).
Question: If this is really how linear regression is defined, why do we say that "linear regression [can]...only generate linear functions such as [lines and planes]"?
For example, if our model for $\hat{Y}$ is as follows:
$$ \hat{Y} = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \ldots + \beta_p X_p $$
then any (or all) of the $X_j$ could be themselves highly non-linear or otherwise pathological functions that take on many bizarre shapes that look nothing like lines or planes. That being the case, a linear combination of those pathological random variables could end up looking like something that fails to resemble a line or a plane. Doesn't this show the quote from above to be false?