How To Take the Composition of Two Functions and Find the Domain and Evaluate

The video tutorial explains the concept of function composition, where one function is applied to the result of another function. It uses the example of f(x) and g(x) to demonstrate how to compose these functions and evaluate the result for a specific value. The tutorial also covers the domain of the composed function, emphasizing that it includes all real numbers unless restricted by division by zero or square roots of negative numbers.

What does it mean to compose two functions?

• To add them together

• To multiply them

• To substitute one into the other

• To divide them

If g(x) = x + 1 and f(x) = 3x + 2, what is the composition f(g(x))?

• 3x + 2

• 3x + 1

• x + 3

• 3(x + 1) + 2

How do you evaluate the composed function 3x + 5 for x = 3?

• Substitute 3 into x and calculate

• Add 3 to the function

• Divide the function by 3

• Multiply the function by 3

What is the result of evaluating the composition f(g(3)) if f(x) = 3x + 5?

• 9

• 17

• 14

• 11

What is the domain of the function 3x + 5?

• Only negative numbers

• Only positive numbers

• All real numbers

• Numbers greater than zero