Evaluating Composite Functions in Mathematics

The video tutorial explains function composition using two functions, g(x) and h(y). It demonstrates how to evaluate h(g(-6)) by first calculating g(-6) and then using that result to find h(3). The tutorial emphasizes understanding the function composition notation and provides a detailed step-by-step calculation to arrive at the final result of 7.

What is the expression for g(x)?

• x^2 - 5x + 3

• x^2 - 3x + 5

• x^2 + 5x - 3

• x^2 + 3x - 5

What is the expression for h(y)?

• 3(y + 1)^2 + 5

• 3(y - 1)^2 + 5

• 3(y + 1)^2 - 5

• 3(y - 1)^2 - 5

What does the small circle between h and g represent?

• Function multiplication

• Function addition

• Function composition

• Function subtraction

How can h(g(-6)) be rewritten for better understanding?

• h of g(-6)

• h(g(-6))

• g(h(-6))

• g(-6) of h

What is the first step in evaluating h(g(-6))?

• Evaluate both simultaneously

• Evaluate h first

• None of the above

• Evaluate g first

What is the value of g(-6)?

• -3

• -7

• 7

• 3

What is the next step after finding g(-6)?

• Subtract 5 from the result

• Input the result into g again

• Input the result into h

• Multiply the result by 2

What is the value of h(3)?

• 7

• 5

• 12

• 3

What is the final result of h(g(-6))?

• 3

• 5

• 7

• 12

What is the correct sequence of steps to solve h(g(-6))?

• None of the above

• Evaluate h first, then g

• Evaluate g first, then h

• Evaluate both simultaneously