https://file.aiquickdraw.com/mathbot/file/17277181749084riqw4tt.jpg

Let's analyze the given functions and solve the problem.

### Functions
- \( f(x) = \frac{12}{\sqrt{x}} \)
- \( g(x) = 3(2x + 1) \)

### Part (a): Find \( g(5) \)
To find \( g(5) \), substitute \( x = 5 \) into \( g(x) \):
\[
g(5) = 3(2 \times 5 + 1) = 3(10 + 1) = 3 \times 11 = 33
\]

### Part (b): Find \( g(f(9)) \)
1. First, find \( f(9) \):
\[
f(9) = \frac{12}{\sqrt{9}} = \frac{12}{3} = 4
\]

2. Next, find \( g(f(9)) = g(4) \):
\[
g(4) = 3(2 \times 4 + 1) = 3(8 + 1) = 3 \times 9 = 27
\]

### Part (c): Find \( g^{-1}(6) \)
To find \( g^{-1}(6) \), we need to find the value of \( x \) such that \( g(x) = 6 \).

\[
3(2x + 1) = 6
\]
Solve for \( x \):
\[
2x + 1 = \frac{6}{3} = 2
\]
\[
2x = 2 - 1 = 1
\]
\[
x = \frac{1}{2}
\]

Thus, \( g^{-1}(6) = \frac{1}{2} \).

Let me know if you'd like more details or have any questions. Here are some related problems to consider:

1. Find \( f(16) \).
2. What is \( g^{-1}(12) \)?
3. Calculate \( f(g(3)) \).
4. Find \( f^{-1}(4) \).
5. Determine the range of \( f(x) \).

**Tip**: When dealing with composite functions, always evaluate the inner function first before substituting into the outer function.

f and g are functions such that f(x) = 12/sqrt(x) and g(x) = 3(2x + 1). Solve the following:
(a) Find g(5).
(b) Find g(f(9)).
(c) Find g^(-1)(6).

Learn how to solve function problems involving f(x) = 12/sqrt(x) and g(x) = 3(2x + 1). This includes finding g(5), g(f(9)), and g^(-1)(6). Step-by-step solutions for high school-level math, suitable for Grades 9-11.

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