Answer:
a) True
Step-by-step explanation:
To prove that g(x) = o(f(x)), we need to show that for any positive constant c, there exists a positive constant k such that for all x > k, |g(x)| < c|f(x)|.
Let's assume c = 1 and find k such that for all x > k, |g(x)| < |f(x)|.
Since f(x) = 3x - 7 and g(x) = x, we have:
|g(x)| = |x|, and
|f(x)| = |3x - 7|.
Now, let's choose k = 7. For any x > k, we can see that:
|g(x)| = |x| < |3x - 7| = |f(x)|.
Therefore, g(x) = o(f(x)).
