https://file.aiquickdraw.com/mathbot/file/1725653189377w650thia.jpg

The image provided contains a mathematical problem involving functions. Let's analyze and solve it step-by-step.

### Given:
1. \( f(x) = x^2 - 5 \)
2. \( g(x) = 6x - 2 \)
3. We need to find \( f(g(2)) \).

### Solution:

To find \( f(g(2)) \), we first need to compute \( g(2) \) and then substitute the result into the function \( f(x) \).

#### Step 1: Calculate \( g(2) \)

\[
g(x) = 6x - 2
\]

Substitute \( x = 2 \):

\[
g(2) = 6(2) - 2 = 12 - 2 = 10
\]

#### Step 2: Calculate \( f(g(2)) = f(10) \)

\[
f(x) = x^2 - 5
\]

Substitute \( x = 10 \):

\[
f(10) = 10^2 - 5 = 100 - 5 = 95
\]

### Conclusion:
The value of \( f(g(2)) \) is **95**.

### Answer:
The correct answer is the orange box: **95**.

Would you like more details or have any questions?

### Related Questions:
1. How do you find the composition of two functions in general?
2. What is the domain and range of the function \( f(x) = x^2 - 5 \)?
3. What is the derivative of the function \( g(x) = 6x - 2 \)?
4. How do you solve for \( x \) when given an equation involving \( f(x) = x^2 - 5 \)?
5. How do you graph the functions \( f(x) = x^2 - 5 \) and \( g(x) = 6x - 2 \)?

### Tip:
When working with composite functions like \( f(g(x)) \), always calculate the inner function first before substituting into the outer function.

f(x) = x^2 - 5 and g(x) = 6x - 2. Find f(g(2)).

Solve the function composition problem where f(x) = x^2 - 5 and g(x) = 6x - 2, and find f(g(2)). This problem involves applying key concepts in function composition and quadratic functions. Suitable for students in Grades 9-10.

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