Operations of Functions and Composite Functions How functions operate Overview ο΄π π₯ ο΄ π+π π₯ ο΄ π−π π₯ ο΄ π·π π₯ ο΄ π/π π₯ ο΄ πβπ π₯ ο΄ πβπ π₯ or π π π₯ or π÷π π₯ π(π₯) ο΄ This is read “f of x” ο΄ For example when we see: π π₯ = 2π₯ 3 − 3π₯ 2 + π₯ − 4 ο΄ Which means function It means whatever we take the “f” of, we need to: of x ο΄ It is usually followed by instructions of what to do with the input (x) ο΄ Take 2 times the input cubed ο΄ Minus 3 times input squared ο΄ Add the input ο΄ Then subtract 4 ο΄ Other common forms ο΄ More simply put, if -2 is the input: are π π₯ πππ β π₯ 3 2 π −2 = 2(−2) − 3 −2 = −34 + (−2) − 4 π+π π₯ ο΄ π + π π₯ is just like saying π π₯ + π(π₯) ο΄Just take one function, put a plus sign and add the second function ο΄For example: π π₯ = 5π₯ 2 + 9 π π₯ = 2π₯ + 10 π + π π₯ → π π₯ + π(π₯) ↓ 5π₯ 2 + 9 + 2π₯ + 10 ↓ 5π₯ 2 + 2π₯ + 19 π−π π₯ ο΄ π − π π₯ is just like saying π π₯ − π(π₯) ο΄ Just write the first function, put a minus sign and place the second function in parentheses after the minus sign ο΄ Remember to distribute the minus sign ο΄ For example: π π₯ = 5π₯ 2 + 9 π π₯ = 2π₯ + 10 π − π π₯ → π π₯ − π(π₯) ↓ 5π₯ 2 + 9 − 2π₯ + 10 ↓ 5π₯ 2 + 9 − 2π₯ − 10 ↓ 5π₯ 2 − 2π₯ − 1 π·π π₯ ο΄ π β π π₯ is just like saying π π₯ × π(π₯) ο΄ Just write the first function in parentheses, place the second function in parentheses after the first function. ο΄ Remember to distribute the terms ο΄ For example: π π₯ = 5π₯ 2 + 9 π π₯ = 2π₯ + 10 π β π π₯ → π π₯ × π(π₯) ↓ 5π₯ 2 + 9 2π₯ + 10 ↓ 10π₯ 3 + 50π₯ 2 + 18π₯ + 90 π/π π₯ ο΄ π/π π₯ is just like saying π π₯ ÷ π(π₯) ο΄ Just write the first function in the numerator, and place the second function in the denominator ο΄ (reduce if possible) ο΄For example: π π₯ = 5π₯ 2 + 9 π π₯ = 2π₯ + 10 π π₯ π/π π₯ → π(π₯) ↓ 5π₯ 2 + 9 2π₯ + 10 πβπ π₯ ο΄ π β π π₯ is just like saying π(π π₯ ) ο΄ Just write the second function in place of x everywhere in the first function ο΄ (simplify if possible) ο΄For example: π π₯ = 5π₯ 2 + 9 π π₯ = 2π₯ + 10 π β π π₯ → π(π π₯ ) ↓ 2 5(2π₯ + 10) +9 ↓ 5 4π₯ 2 + 40π₯ + 100 + 9 πβπ π₯ ο΄ π β π π₯ is just like saying π(π π₯ ) ο΄ Very similar to π β π π₯ , but instead of 2 different functions: ο΄ Just write the function in place of x everywhere in the first function ο΄ (simplify if possible) ο΄For example: π π₯ = 5π₯ 2 + 9 π β π π₯ → π(π π₯ ) ↓ 2 2 5(5π₯ + 9 ) +9 ↓ 5 25π₯ 4 + 90π₯ 2 + 81 + 9