Verified Answer :

e3van22

To evaluate \( (h \circ f)(-3) \), where \( f(x) = \frac{3}{x} - 4 \) and \( h(x) = \frac{1}{3}x^2 - 2 \), we first need to find the value of \( f(-3) \), and then plug this value into the function \( h(x) \).

1. Evaluate \( f(-3) \):

\[ f(-3) = \frac{3}{-3} - 4 = -1 - 4 = -5 \]

2. Now, evaluate \( h(-5) \):

\[ h(-5) = \frac{1}{3}(-5)^2 - 2 = \frac{1}{3}(25) - 2 = \frac{25}{3} - 2 \]

\[ = \frac{25}{3} - \frac{6}{3} = \frac{25 - 6}{3} = \frac{19}{3} \]

So, \( (h \circ f)(-3) = \frac{19}{3} \).

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