Determining Functions and Decomposition

Determining Functions and Decomposition

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Hard

Created by

Thomas White

FREE Resource

The video tutorial explains how to solve a function problem involving composite functions. It begins with an introduction to the problem, where FX and GX are given, and the composite function G(FX) is provided. The tutorial then delves into understanding composite functions and the process of decomposition. The instructor provides a step-by-step solution to find GX by decomposing the given composite function. The video concludes with the final steps and a summary of the solution, ensuring clarity in understanding the process.

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15 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main objective of the problem discussed in the video?

To calculate the derivative of g(x)

To find the value of x

To determine the function g(x)

To solve for f(x)

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the given expression for f(x)?

f(x) = x^2 - 1

f(x) = 3x - 2

f(x) = 2x + 3

f(x) = 5x + 4

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the expression for g(f(x)) provided in the problem?

g(f(x)) = 2x - 5

g(f(x)) = 6x - 1

g(f(x)) = 5x + 2

g(f(x)) = 4x + 3

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in decomposing the composite function?

Differentiate g(f(x))

Integrate f(x)

Substitute f(x) into g(f(x))

Solve for x

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the expression for g(x) after substituting f(x) into g(f(x))?

g(x) = 6x - 1

g(x) = 2(3x - 2) + 3

g(x) = 3x - 2

g(x) = 2x + 1

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What operation is performed to equate the expressions for g(f(x))?

Division

Multiplication

Subtraction

Addition

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value added to balance the equation for g(x)?

3

2

1

4

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