Exploring Composite Functions and Their Values

This video tutorial introduces composite functions, explaining them as combinations of two functions. It emphasizes the importance of the order in which functions are composed, as it affects the output. The video provides a formal definition and notation for composite functions, distinguishing it from multiplication. Through examples, it demonstrates how to evaluate composite functions and substitute one function into another. The tutorial concludes with a brief introduction to inverse functions, highlighting their special relationship when F of G equals G of F.

What is the final output when the input 3 is first squared by function F and then multiplied by 2 by function G?

• 18

• 9

• 6

• 36

If the order of functions is reversed, what is the output when the input 3 is first multiplied by 2 by function G and then squared by function F?

• 18

• 9

• 6

• 36

What symbol is used to denote the composition of functions?

• Plus sign

• Multiplication sign

• Solid circle

• Hollow circle

In the notation F(G(x)), which function is evaluated first?

• It depends on the input

• Both simultaneously

• G

• F

What is the value of F(G(3)) if G(x) = x^3 - 5 and F(x) = 2x - 1?

• 43

• 22

• 120

• 36

What is the value of G(F(3)) if F(x) = 2x - 1 and G(x) = x^3 - 5?

• 120

• 43

• 22

• 36

What is the value of H(G(-1)) if G(x) = x^3 - 5 and H(x) = 5 - x^2?

• 6

• 31

• -31

• -6

How do you evaluate F(G(x)) when no specific input is given?

• By using the average value

• By guessing

• By replacing G(x) with its entire function

• By substituting a random value

What is the result of F(G(x)) if F(x) = 4x + 1 and G(x) = x^2 - x + 5?

• 4x + 1

• 4x^2 + x + 5

• x^2 - x + 5

• 4x^2 - 4x + 21

What is the result of G(F(x)) if F(x) = 4x + 1 and G(x) = x^2 - x + 5?

• 16x^2 + 4x + 5

• 4x^2 - 4x + 21

• 16x^2 + 4x + 4

• 4x + 1