Composition of Functions Problems

This video tutorial from the Matematika Hebat channel covers six models of composition function problems. Each model is explained step-by-step, demonstrating how to solve for F Bundaran GX, G Bundaran FX, G Bundaran F2, G Bundaran Fa, and how to determine functions GX and FX. The tutorial aims to provide clear solutions and encourage viewers to engage with the material through practice problems.

What is the main topic discussed in the video?

• Trigonometric functions

• Quadratic equations

• Composition functions

• Linear equations

In the first problem type, what is the expression for F(G(x)) if G(x) = 5x + 6 and F(x) = 2x² + 7?

• 5x² + 2x + 7

• 2x² + 5x + 6

• 5(2x² + 7) + 6

• 2(5x + 6)² + 7

For the second problem type, if F(x) = 3x² + 5x - 6 and G(x) = 5x - 3, what is G(F(x))?

• 5(3x² + 5x - 6) - 3

• 3(5x - 3)² + 5x - 6

• 5x² + 3x - 6

• 3x² + 5x - 3

In the third problem type, what is the first step to find G(F(2))?

• Multiply F(x) and G(x)

• Find the inverse of F(x)

• Calculate F(2) first

• Directly substitute 2 into G(x)

In the fourth problem type, if G(F(a)) = 23, what is the value of 'a' when G(x) = 5x + 3 and F(x) = 3x - 5?

• 2

• 3

• 4

• 5

In the fifth problem type, if F(G(x)) = x² + 2x - 2 and F(x) = x² - 3, what is G(x)?

• x + 1

• x - 1

• x² + 1

• x² - 1

In the sixth problem type, if F(G(x)) = 4x - 2 and G(x) = 4x - 5, what is F(x)?

• 2x - 3

• 2x + 3

• x - 3

• x + 3