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Let's solve the problem.

We are given:
\[
(f \circ g)(x) = 9x^2 - 6x - 3
\]
and
\[
g(x) = 3x - 1.
\]
We need to find the value of \( f^{-1}(12) \).

### Step 1: Determine \( f(x) \)
Since \( (f \circ g)(x) = f(g(x)) \), we substitute \( g(x) = 3x - 1 \) into \( f(g(x)) = 9x^2 - 6x - 3 \) to find \( f(x) \).

Let \( u = g(x) = 3x - 1 \). Then,
\[
f(u) = 9x^2 - 6x - 3.
\]

To express \( f \) in terms of \( u \), solve \( x \) in terms of \( u \) from \( u = 3x - 1 \):
\[
x = \frac{u + 1}{3}.
\]
Substitute this expression for \( x \) back into \( f(g(x)) \):
\[
f(u) = 9\left(\frac{u + 1}{3}\right)^2 - 6\left(\frac{u + 1}{3}\right) - 3.
\]

Expanding and simplifying gives \( f(u) \).

### Step 2: Find \( f^{-1}(12) \)
Once

Diketahui (f ∘ g)(x) = 9x^2 - 6x - 3. Jika g(x) = 3x - 1, nilai dari f^{-1}(12) = …

Learn how to solve for f^{-1}(12) in a composition of functions problem where (f ∘ g)(x) = 9x^2 - 6x - 3 and g(x) = 3x - 1. This solution demonstrates key concepts in inverse functions and composition of functions, suitable for advanced high school math students.

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