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Kindly refer to the diagram shown below as a way to help students understand the concept of functions better.

It has been claimed that composite functions has caused a lot of confussion amongst students, and as such I’ve summarised the 3 different type of composite functions and its way of solving each and every type. InsyaAllah I’ll try to post some SPM standard questions and solutions for your further reference in the near future. I hope I have done enough to ease the difficulties faced by most students.

This posting goes specifically to Humairaa and all my students in Mawar Alam Budiman, Subang Perdana, Section 9 and not forgetting my beloved daughter Dayang Souraya and her comrades, Dania, Sharifah Inaz, Batrisya & Aniq of SMK Bukit Jelutong🙂

function

function1

function2

Pelajar dinasihatkan untuk membuat penelitian dalam contoh soalan Composite Functions yang melibatkan Type 2 dengan Type 3. Try to identify what makes the two different from one to another.

Kesimpulan yang Uncle boleh share dengan kesemua pelajar adalah seperti berikut:

TYPE 2 : Given f(x) and fg(x)

  • the basic function of f(x) is given and mentioned first in the the composite function of fg(x) OR
  • the question require solution on the function g(x) which is mentioned second in the composite function of fg(x)

TYPE 3 : Given is g(x) and fg(x)

  • the basic function of g(x) is given and mentioned second in the composite function of fg(x) OR
  • the question require solution on the function f(x) which is mentioned first in the composite function of fg(x)

function3