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    IB Math AASL
    /
    Function Theory
    /

    Video

    Video Reviews

    Watch comprehensive video reviews for most units, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    Function Theory

    Video Reviews

    Watch comprehensive video reviews for Function Theory, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    Function graphsComposite & inverse functions (SL +HL)Problem Solving SL+HLHL only

    The video will automatically pause when it reaches a problem.

    Composite functions

    SL AA 2.5

    Functions can be composed by passing the output of one into the other. We use the symbol ∘, and pay close attention to the order in which functions are composed:

    (f∘g)(x)=f(g(x))🚫


    Example

    Given f(x)=x2 and g(x)=2x−1, find (a) (f∘g)(x) and (b) (g∘f)(x).


    (f∘g)(x)=(2x−1)2=4x2−4x+1


    (g∘f)(x)=2x2−1

    Composite functions

    SL AA 2.5

    Functions can be composed by passing the output of one into the other. We use the symbol ∘, and pay close attention to the order in which functions are composed:

    (f∘g)(x)=f(g(x))🚫


    Example

    Given f(x)=x2 and g(x)=2x−1, find (a) (f∘g)(x) and (b) (g∘f)(x).


    (f∘g)(x)=(2x−1)2=4x2−4x+1


    (g∘f)(x)=2x2−1
    Function graphsComposite & inverse functions (SL +HL)Problem Solving SL+HLHL only