The image contains three mathematical problems, each requiring evaluation of given functions and statements to determine if they are true or false.

Problem 10

The problem provides functions $f$ and $g$ with compositions such as $(f \circ g)(x)$ and specific values. The task is to verify the statements (A-E) based on these compositions.

Given dataThe image contains three mathematical problems, each requiring evaluation of given functions and statements to determine if they are true or false.

Problem 10

The problem provides functions $f$ and $g$ with compositions such as $(f \circ g)(x)$ and specific values. The task is to verify the statements (A-E) based on these compositions.

Given

1. $g(x) = x + 2$
2. $f(x) = x^2 + 3x - 15$

The statements are:

• $(f \circ g)(x) = x^2 + 7x - 5$
• Evaluating specific values and compositions of $g$ and $f$ at given points.

Problem 11

Here, the functions $f$ and $g$ are also defined, and the question lists several statements to classify as true or false.

Given dataThe image contains three mathematical problems, each requiring evaluation of given functions and statements to determine if they are true or false.

Problem 10

The problem provides functions $f$ and $g$ with compositions such as $(f \circ g)(x)$ and specific values. The task is to verify the statements (A-E) based on these compositions.

Given

1. $g(x) = x + 2$
2. $f(x) = x^2 + 3x - 15$

The statements are:

• $(f \circ g)(x) = x^2 + 7x - 5$
• Evaluating specific values and compositions of $g$ and $f$ at given points.

Problem 11

Here, the functions $f$ and $g$ are also defined, and the question lists several statements to classify as true or false.

Given

1. $f(x) = 2x - 3$
2. $g(x) = 3x + 1$

Statements involve compositions and specific function evaluations, such as:

• $(f \circ g)(x) = 2x^2 + 10x + 5$
• Specific values for compositions like $(g \circ f)(-2) = 3$

Problem 12

This question requires checking the validity of equations involving function compositions and inverses, with options (A-E) listing various composite and inverse operations.

Let me know if you'd like me to go through each statement step-by-step to determine their truth values and provide detailed explanations for each answer.

Follow-Up Questions

1. Would you like to understand how to compute function compositions?
2. Do you need clarification on how to find inverse functions?
3. Are you interested in learning techniques to evaluate specific values of composed functions?
4. Would you like to go over the principles of verifying true or false statements in algebraic functions?
5. Do you need assistance in understanding how function operations impact graph shapes?

Tip: When dealing with function compositions, always substitute one function into the other carefully, following the given order of operations.