functions (A-level only) Flashcards","topicId":"2a53c63b-714a-4b92-83d4-cacc5e0717cb","topicSlug":"composite-functions","cards":[{"id":"c135deb4-3b2d-4943-834e-5fbcfe326a90","cardType":"cloze","front":"In $f(g(x))$, apply [ ].","back":"In $f(g(x))$, apply $g$ first.","points":null,"mcqOptions":null},{"id":"e613eeb3-3b3b-456d-bae2-0a038a91c565","cardType":"cloze","front":"The notation $fg(x)$ means $\\text{[...]}$.","back":"The notation $fg(x)$ means $\\boxed{f(g(x))}$.","points":null,"mcqOptions":null},{"id":"0aea99e1-8638-4bf0-b3d4-00927c2c8e06","cardType":"basic","front":"If $f(x)=2x+3$, what is $f(a-1)$?","back":"$2a+1$","points":1,"mcqOptions":null},{"id":"f6fbcdbb-937a-4e90-9073-69b634358210","cardType":"basic","front":"If $f(x)=3x-4$ and $g(x)=x^2+2$, which function acts first in $fg(x)$?","back":"$g$ acts first.","points":1,"mcqOptions":null},{"id":"e9df4ca8-a174-40dd-92b0-e7de76742ad1","cardType":"basic","front":"If $f(x)=3x-4$ and $g(x)=x^2+2$, find $fg(x)$.","back":"$3x^2+2$","points":2,"mcqOptions":null},{"id":"8c7e728c-3825-41bf-8076-bc54d9163f7f","cardType":"basic","front":"If $f(x)=3x-4$ and $g(x)=x^2+2$, find $fg(-2)$.","back":"$14$","points":2,"mcqOptions":null},{"id":"13237682-2262-4156-8d91-a335e229caf4","cardType":"cloze","front":"Function composition is usually [ ], so $fg(x)\\neq gf(x)$ in general.","back":"Function composition is usually not commutative, so $fg(x)\\neq gf(x)$ in general.","points":null,"mcqOptions":null},{"id":"fed59012-9fad-4b66-8f60-320280ca2ed5","cardType":"basic","front":"If $f(x)=2x+1$ and $g(x)=x^2$, find $fg(x)$.","back":"$2x^2+1$","points":2,"mcqOptions":null},{"id":"71b3ff19-7bff-4731-b792-0fbfe67a393d","cardType":"basic","front":"If $f(x)=2x+1$ and $g(x)=x^2$, find $gf(x)$.","back":"$(2x+1)^2$","points":2,"mcqOptions":null},{"id":"6a336fd4-89fc-4d28-9be9-afcd5b282f38","cardType":"basic","front":"Why do $fg$ and $gf$ usually produce different functions?","back":"They apply the functions in a different order.","points":2,"mcqOptions":null},{"id":"96c180ce-19e5-4b03-898a-c7ae989fd4ed","cardType":"cloze","front":"In composition notation, $f^2(x)$ means $\\text{[...]}$, not $(f(x))^2$.","back":"In composition notation, $f^2(x)$ means $\\boxed{f(f(x))}$, not $(f(x))^2$.","points":null,"mcqOptions":null},{"id":"9e359328-52cc-4323-8576-a09d57f7618e","cardType":"basic","front":"If $f(x)=2x-3$, find $f^2(x)$.","back":"$4x-9$","points":2,"mcqOptions":null},{"id":"5c1a7497-29b2-4375-9e0c-2e374c595015","cardType":"basic","front":"What restriction must be imposed when a composite function has a denominator?","back":"The denominator must be non-zero.","points":1,"mcqOptions":null},{"id":"524a8f2a-d54d-4434-a605-a8dd02b3beb3","cardType":"basic","front":"What restriction must be imposed when a real-valued composite function contains a square root?","back":"The radicand must be greater than or equal to zero.","points":1,"mcqOptions":null},{"id":"9d14bb6d-dc22-458e-9adc-e22809b73c8b","cardType":"cloze","front":"For $f(g(x))$ to exist, $g(x)$ must lie in the [ ].","back":"For $f(g(x))$ to exist, $g(x)$ must lie in the domain of $f$.","points":null,"mcqOptions":null},{"id":"4bab0691-5c01-4bcf-821e-4912f5689efa","cardType":"basic","front":"If $f(x)=\\frac{1}{x-3}$ and $g(x)=x^2+1$, find $fg(x)$.","back":"$\\frac{1}{x^2-2}$","points":2,"mcqOptions":null},{"id":"a5b32f46-ff8a-42e4-b3d3-ed3e13cf3ca2","cardType":"basic","front":"State the domain restriction for $fg(x)=\\frac{1}{x^2-2}$.","back":"$x\\neq\\pm\\sqrt{2}$","points":2,"mcqOptions":null},{"id":"0b46cb1a-a970-4a82-a

1.3.4 Composite functions (A-level only) Flashcards

1.3.4 Composite functions (A-level only) Flashcards