Lesson Worksheet: Operations on Functions Mathematics

In this worksheet, we will practice adding, subtracting, multiplying, and dividing two functions and finding the composition of functions.


If ๐‘“(๐‘ฅ)=๐‘ฅ+5 and ๐‘”(๐‘ฅ)=๐‘ฅโˆ’2๏Šจ, then find and fully simplify an expression for (๐‘“+๐‘”)(๐‘ฅ).

  • A๐‘ฅ+๐‘ฅโˆ’3๏Šจ
  • B๐‘ฅ+๐‘ฅโˆ’2๏Šจ
  • C๐‘ฅ+๐‘ฅ+3๏Šจ
  • D๐‘ฅ+๐‘ฅโˆ’7๏Šจ
  • E๐‘ฅ+๐‘ฅ+5๏Šจ


If ๐‘“ and ๐‘” are two real functions where ๐‘“(๐‘ฅ)=๐‘ฅโˆ’1๐‘ฅ+3๐‘ฅโˆ’4๏Šจ and ๐‘”(๐‘ฅ)=๐‘ฅ+3, determine the value of (๐‘“+๐‘”)(โˆ’4) if possible.

  • Aโˆ’65
  • Bโˆ’6
  • Cundefined
  • Dโˆ’1


Given that ๐‘›(๐‘ฅ)=๐‘ฅ+16๐‘ฅโˆ’8๏Šง, ๐‘›(๐‘ฅ)=9๐‘ฅ+144๐‘ฅโˆ’8๏Šจ, and ๐‘›(๐‘ฅ)=๐‘›(๐‘ฅ)รท๐‘›(๐‘ฅ)๏Šง๏Šจ, determine ๐‘›(๐‘ฅ) in its simplest form.

  • A๐‘›(๐‘ฅ)=19
  • B๐‘›(๐‘ฅ)=9
  • C๐‘›(๐‘ฅ)=29
  • D๐‘›(๐‘ฅ)=16
  • E๐‘›(๐‘ฅ)=116


Find โ„Ž(๐‘ฅ), where โ„Ž(๐‘ฅ)=๐‘”โˆ˜๐‘“(๐‘ฅ) and ๐‘“(๐‘ฅ)=๐‘ฅโˆ’๐‘ฅโˆ’1๏Šจ, ๐‘”(๐‘ฅ)=๐‘ฅ+1.

  • A๐‘ฅโˆ’๐‘ฅ๏Šจ
  • B๐‘ฅ๏Šจ
  • C๐‘ฅ+๐‘ฅ๏Šจ
  • D๐‘ฅโˆ’2๐‘ฅ๏Šจ
  • E๐‘ฅ


If ๐‘“(๐‘ฅ)=๏„ž๐‘ฅ+52๏Žข and ๐‘”(๐‘ฅ)=2๐‘ฅโˆ’5๏Šฉ, then ๐‘”(๐‘“(๐‘ฅ))=.

  • A5(๐‘ฅ+5)
  • B๐‘ฅโˆ’5๏Šฉ
  • C1.5(๐‘ฅ+5)
  • D๐‘ฅ


Given that ๐‘“ and ๐‘” are two real functions where ๐‘“(๐‘ฅ)=๐‘ฅโˆ’1๏Šจ and ๐‘”(๐‘ฅ)=โˆš๐‘ฅ+5, find the value of ๏€ฝ๐‘”๐‘“๏‰(โˆ’2) if possible.

  • Aโˆš3
  • B3
  • Cโˆ’โˆš33
  • Dundefined
  • Eโˆš33


Given that ๐‘“โˆถโ„โ†’โ„๏Šฐ, where ๐‘“(๐‘ฅ)=๐‘ฅโˆ’19, and ๐‘”โˆถ[โˆ’2,13]โ†’โ„, where ๐‘”(๐‘ฅ)=๐‘ฅโˆ’6, evaluate (๐‘“โ‹…๐‘”)(7).

  • Aโˆ’774
  • Bโˆ’240
  • C724
  • Dโˆ’12


If ๐‘“ and ๐‘” are two real functions where ๐‘“(๐‘ฅ)=๐‘ฅ+9๐‘ฅ+15๐‘ฅ+54๏Šจ and ๐‘”(๐‘ฅ)=๐‘ฅ+8, determine the value of (๐‘“โˆ’๐‘”)(โˆ’6) if possible.

  • Aโˆ’2
  • Bundefined
  • C1
  • Dโˆ’53


Find (๐‘“โˆ’๐‘”)(๐‘ฅ) given ๐‘“(๐‘ฅ)=๐‘ฅโˆ’2๏Šจ and ๐‘”(๐‘ฅ)=๐‘ฅโˆ’5.

  • A๐‘ฅโˆ’๐‘ฅโˆ’7๏Šจ
  • Bโˆ’๐‘ฅ+๐‘ฅโˆ’3๏Šจ
  • C๐‘ฅโˆ’๐‘ฅ+3๏Šจ
  • D๐‘ฅโˆ’๐‘ฅ+7๏Šจ
  • E๐‘ฅ+๐‘ฅ+3๏Šจ


Given that ๐‘“(๐‘ฅ)=3๐‘ฅ+2, find ๐‘”(๐‘ฅ)=๐ด๐‘ฅ+๐ต so that (๐‘“โˆ˜๐‘”)(๐‘ฅ)=1โˆ’๐‘ฅ.

  • A๐‘”(๐‘ฅ)=โˆ’3๐‘ฅโˆ’3
  • B๐‘”(๐‘ฅ)=โˆ’๐‘ฅ+1
  • C๐‘”(๐‘ฅ)=โˆ’13๐‘ฅ+1
  • D๐‘”(๐‘ฅ)=โˆ’4๐‘ฅโˆ’1
  • E๐‘”(๐‘ฅ)=โˆ’13๐‘ฅโˆ’13

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