Understanding Composite Functions

The video tutorial explains composite functions, where the output of one function becomes the input of another. It provides four examples: F of G of 2, G of F of 4, F of G of 1/2, and F of F of -4/5, demonstrating step-by-step calculations for each. The tutorial emphasizes understanding the process of substitution and finding common denominators in fractions.

What is the main idea behind a composite function?

• Combining two functions into one.

• Using the output of one function as the input of another.

• Differentiating a function twice.

• Finding the inverse of a function.

In the example F(G(2)), what is the value of G(2)?

• 11

• 9

• 7

• 5

What is the final result of F(G(2))?

• 21/5

• 41/5

• 12/5

• 32/5

In the example G(F(4)), what is the value of F(4)?

• 32/5

• 12/5

• 21/5

• 41/5

What is the final result of G(F(4))?

• 1473/25

• 1048/25

• 800/25

• 225/25

In the example F(G(1/2)), what is the value of G(1/2)?

• 6

• 5

• 7

• 8

What is the final result of F(G(1/2))?

• 12/5

• 21/5

• 41/5

• 32/5

In the example F(F(-4/5)), what is the value of F(-4/5)?

• 100/25

• 64/25

• 88/25

• 76/25

What is the final result of F(F(-4/5))?

• 125/125

• 264/125

• 500/125

• 764/125

What is the common denominator used in the calculation of F(F(-4/5))?

• 125

• 25

• 5

• 100