Exploring Adding and Subtracting Rational Expressions

The video tutorial covers function operations, including addition, subtraction, multiplication, and division of functions. It explains operation rules and provides examples, highlighting the importance of domain restrictions, especially when dividing functions. The tutorial also introduces compositions of functions, demonstrating how to substitute one function into another. Throughout, the video emphasizes understanding notation and applying these concepts through practical examples.

What does the notation f + g(x) represent?

• f(x) multiplied by g(x)

• f(x) divided by g(x)

• f(x) subtracted from g(x)

• f(x) added to g(x)

If f(x) = x^2 - 8x + 4 and g(x) = 4x - 3, what is f + g(x)?

• x^2 - 8x + 7

• x^2 - 4x + 1

• x^2 - 12x + 7

• x^2 - 4x - 1

When dividing functions, why must we define the domain?

• To ensure the functions are continuous

• To avoid dividing by zero

• To simplify the functions

• To find the range of the functions

What is the result of f - h(x) if f(x) = x^2 - 8x + 4 and h(x) = x + 2?

• x^2 - 8x + 6

• x^2 - 9x + 6

• x^2 - 9x + 2

• x^2 - 7x + 2

How do you evaluate f + g at a specific value, say x = -2?

• Find f(x) and g(x) separately at x = -2, then add the results

• Find f(x) and g(x) separately at x = -2, then multiply the results

• Find f(x) and g(x) separately at x = -2, then subtract the results

• Find f(x) and g(x) separately at x = -2, then divide the results

What is the composite function f o g(x) defined as?

• f(x) - g(x)

• f(x) + g(x)

• g(f(x))

• f(g(x))

If f(x) = 5x - 3 and g(x) = x - 1, what is f(g(x))?

• 5x - 2

• 5x - 4

• 5x - 8

• 5x - 6

What is the result of g(h(x)) if g(x) = x - 1 and h(x) = x^3 + 8?

• x^3 + 6

• x^3 + 9

• x^3 + 7

• x^3 + 8

How do you evaluate g(f(2)) if f(x) = 5x - 3 and g(x) = x - 1?

• Find g(2) first, then substitute into f(x)

• Multiply f(2) and g(2)

• Find f(2) first, then substitute into g(x)

• Add f(2) and g(2)

What is the value of f(h(-6)) if f(x) = 5x - 3 and h(x) = x^3 + 8?

• -1043

• -1045

• -1042

• -1040