Finding the Inverse Function of a Composite Function

Finding the Inverse Function of a Composite Function

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Practice Problem

Hard

Created by

Wayground Content

FREE Resource

The video tutorial explains how to calculate the inverse function of H, given that H equals the composition of two functions, F and G. The process involves substituting G into F, rearranging the resulting equation to isolate X, and then factorizing and simplifying the equation. The final step is to express the inverse function of H in terms of X. The tutorial also outlines the marking scheme for the problem, emphasizing the importance of each step in the process.

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7 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the initial step in finding the inverse of H given functions F and G?

Add F and G

Multiply F and G

Substitute G into F

Substitute F into G

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

After substituting G into F, what is the next step to simplify the expression?

Divide by the numerator

Multiply by the denominator

Subtract 1 from both sides

Add 1 to both sides

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the purpose of rearranging the equation in the process of finding the inverse?

To simplify the fraction

To isolate the variable X

To eliminate the variable Y

To add constants to both sides

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which operation is used to separate X from Y in the equation XY - X?

Factorization

Subtraction

Addition

Division

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the final form of the inverse function of H?

X + 1 / 2

3 - X / X - 1

1 + 1 / X

X - 1 / 3

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How many marks are allocated for correctly identifying the substitution of G into F?

Two marks

Four marks

One mark

Three marks

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the final step in confirming the inverse function of H?

Subtract X from both sides

Multiply by the denominator

Add 1 to both sides

Substitute Y back to X

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