Finding the Inverse Function of a Composite Function

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.

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

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

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

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

• Factorization

• Subtraction

• Addition

• Division

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

• X + 1 / 2

• 3 - X / X - 1

• 1 + 1 / X

• X - 1 / 3

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

• Two marks

• Four marks

• One mark

• Three marks

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