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.