Exploring Function Operations and Compositions

This video tutorial covers function operations and compositions, including addition, subtraction, multiplication, and division of functions. It explains domain restrictions and explores power functions. The tutorial includes examples of calculating profit and wages using function operations and compositions, providing a practical understanding of these mathematical concepts.

What is the result of adding two functions f(x) = 5x and g(x) = x?

• 6x

• 5x + x

• 5x - x

• 5x * x

When subtracting two functions, what must you remember to do?

• Divide the functions

• Distribute the negative sign

• Add the functions first

• Multiply the functions

What is the domain restriction when dividing f(x) by g(x)?

• f(x) must be positive

• g(x) must be positive

• g(x) cannot be zero

• f(x) cannot be zero

What is the result of adding f(x) = 5x^(1/3) and g(x) = -11x^(1/3)?

• 16x^(1/3)

• -16x^(1/3)

• 6x^(1/3)

• -6x^(1/3)

What is the domain of f(x) = x^(1/2)?

• All real numbers

• x > 0

• x >= 0

• x < 0

What is the result of multiplying 8x by 2x^(5/6)?

• 8x^(11/6)

• 16x^(5/6)

• 8x^(5/6)

• 16x^(11/6)

In a composition of functions, what is the domain of the composed function?

• The domain of the first function

• The intersection of the domains of both functions

• The domain of the second function

• The union of the domains of both functions

What is the result of the composition f(g(-3)) if f(x) = 3x - 4 and g(x) = x^2 - 1?

• 24

• 16

• 20

• 8

If you receive a 5% raise followed by a $0.75 raise, what is your new hourly wage if you initially earned $6 per hour?

• $6.75

• $6.30

• $7.09

• $7.05

Which order of applying raises results in a higher final wage: 5% raise first or $0.75 raise first?

• Both result in the same wage

• 5% raise first

• $0.75 raise first

• Neither affects the final wage