Exploring Composite Functions in GCSE Maths

This video tutorial covers the concept of composite functions, demonstrating how to calculate G(F(x)) and F(G(x)) through examples. It also includes practice questions and explains how to write expressions for composite functions. The video concludes with a section on finding inverse functions.

What is the first step in finding G(F(4)) given F(x) = 3x - 5 and G(x) = 2x + 4?

• Substitute 4 into G

• Multiply 4 by G

• Add 4 to F

• Substitute 4 into F

If F(4) = 7, what is the next step to find G(F(4))?

• Subtract 7 from G

• Substitute 7 into G

• Add 7 to G

• Multiply 7 by G

Given F(x) = 2x + 5 and G(x) = x^2 - 5, what is the first step to find F(G(3))?

• Substitute 3 into G

• Add 3 to G

• Multiply 3 by F

• Substitute 3 into F

If G(3) = 4, what is the next step to find F(G(3))?

• Subtract 4 from F

• Multiply 4 by F

• Add 4 to F

• Substitute 4 into F

What is the expression for F(G(x)) given F(x) = x^2 + 4 and G(x) = 2x + 1?

• (2x + 1)^2 + 4

• 2x^2 + 1 + 4

• x^2 + 2x + 1

• 2(x^2 + 4)

What is the simplified form of F(G(x)) for F(x) = x^2 + 4 and G(x) = 2x + 1?

• 4x^2 + 4x + 9

• 4x^2 + 4x + 5

• 4x^2 + 4x + 4

• 4x^2 + 4x + 1

What is the expression for G(F(x)) given F(x) = x^2 + 4 and G(x) = 2x + 1?

• 2x^2 + 4 + 1

• 2(x^2 + 4) + 1

• 2(x + 4) + 1

• 2x + 4 + 1

What is the simplified form of G(F(x)) for F(x) = x^2 + 4 and G(x) = 2x + 1?

• 2x^2 + 8 + 1

• 2x^2 + 8 + 4

• 2x^2 + 8 + 5

• 2x^2 + 8 + 9

Given H(x) = 6x + 8, what is the first step to find the inverse function of H?

• Set H(x) equal to y

• Set H(x) equal to x

• Set H(x) equal to 0

• Set H(x) equal to 1

What is the inverse function of H(x) = 6x + 8?

• (x - 8) / 6

• (x + 8) / 6

• (x - 6) / 8

• (x + 6) / 8