Composition of Two Functions

The video tutorial explains the concept of function composition, focusing on F of G of X and G of F of X. It provides examples of evaluating functions with various inputs and demonstrates how to apply function composition to solve mathematical problems. The tutorial emphasizes following patterns in function evaluation and composition.

What is the result of switching the order of functions in a composition from F(G(x)) to G(F(x))?

• The functions become equal.

• The order of operations is reversed.

• The composition becomes undefined.

• The functions are evaluated separately.

How do you evaluate G(-1) if G(x) = -4x + 5?

• Subtract -1 from the function.

• Replace x with -1 and solve.

• Multiply the function by -1.

• Add -1 to the function.

What is the first step in evaluating G(3P) for G(x) = -4x + 5?

• Multiply 3P by 5.

• Replace x with 3P.

• Add 3P to the function.

• Divide the function by 3P.

When substituting F(x) into G(x) to find G(F(x)), what is the expression if F(x) = 2x?

• -4x + 5

• -8x + 5

• 2(-4x + 5)

• -4(2x) + 5

What is the final expression for G(F(x)) if F(x) = 2x and G(x) = -4x + 5?

• -8x + 10

• -8x + 5

• -4x + 10

• -4x + 5