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We are given two functions: 

- \( f(x) = 3x - 1 \)
- \( g(x) = x^2 - 1 \)

The task is to find \( (f \circ g)(-5) \), which means we need to evaluate \( f(g(-5)) \).

### Step 1: Find \( g(-5) \)
Substitute \( x = -5 \) into the function \( g(x) = x^2 - 1 \):
\[
g(-5) = (-5)^2 - 1 = 25 - 1 = 24
\]

### Step 2: Find \( f(g(-5)) = f(24) \)
Now, substitute \( g(-5) = 24 \) into the function \( f(x) = 3x - 1 \):
\[
f(24) = 3(24) - 1 = 72 - 1 = 71
\]

Thus, \( (f \circ g)(-5) = 71 \).

Would you like further details on any of the steps? 

Here are 5 related questions for further practice:
1. What is \( g(f(x)) \) when \( x = 2 \)?
2. Find \( (f \circ g)(3) \).
3. If \( f(x) = 2x + 3 \) and \( g(x) = x^2 + 2x \), find \( (f \circ g)(-1) \).
4. What is the inverse function of \( f(x) = 3x - 1 \)?
5. Solve for \( x \) when \( f(g(x)) = 0 \).

**Tip**: In composition of functions, always apply the inner function first, then use the result in the outer function!

Let f(x) = 3x - 1 and g(x) = x^2 - 1. Find (f o g)(-5).

Learn how to calculate the composition of functions using quadratic and linear formulas. This example involves evaluating f(g(-5)) by substituting x = -5 in g(x) and using the result in f(x), illustrating how functions can be combined algebraically.

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