Type":"basic","front":"How do you evaluate $h(4)$ for the function $h(x) = 2x^2 - 6$?","back":"Substitute 4 for $x$ in the formula: $2(4)^2 - 6$.","points":1},{"id":"473f7bb3-5d80-41ba-a7da-27d33798bfaf","cardType":"cloze","front":"When substituting negative numbers into a function, always use [ ] to avoid calculation errors.","back":"When substituting negative numbers into a function, always use brackets to avoid calculation errors.","points":null},{"id":"7a9cb8f2-28c3-44a1-aa79-089e41c49ce1","cardType":"basic","front":"What does the instruction \"solve $f(x) = 10$\" mean?","back":"Find the input values that result in an output of 10.","points":1},{"id":"30312376-eab2-46e3-8fa7-39310234ab9a","cardType":"basic","front":"If $x^2 = 9$, why are there two possible solutions for $x$?","back":"Both positive and negative values give a positive result when squared ($3^2 = 9$ and $(-3)^2 = 9$).","points":1},{"id":"d61e892c-0dc9-475c-a5a5-909ac45cd7bd","cardType":"basic","front":"What is the relationship between the outputs of $f(x)$ and $f^{-1}(x)$?","back":"The inverse function $f^{-1}$ undoes the function $f$ (if $f(a) = b$, then $f^{-1}(b) = a$).","points":1},{"id":"015d4405-d6e8-4fe9-ad7f-ab5f3092fd58","cardType":"basic","front":"Outline the three steps to find an inverse function $f^{-1}(x)$.","back":"

Set $y = f(x)$
Swap $x$ and $y$
Rearrange the equation to make $y$ the subject

","points":3},{"id":"3c8e3880-9886-4c88-b56f-f26c29df2688","cardType":"cloze","front":"The notation $f^{-1}(x)$ refers to the [ ], not the reciprocal ($\\frac{1}{f(x)}$).","back":"The notation $f^{-1}(x)$ refers to the inverse function, not the reciprocal ($\\frac{1}{f(x)}$).","points":null},{"id":"43f86764-376f-4e03-8330-2ce9a849e78b","cardType":"cloze","front":"The notation $f^{-1}(x)$ refers to the inverse function, not the [ ] ($\\frac{1}{f(x)}$).","back":"The notation $f^{-1}(x)$ refers to the inverse function, not the reciprocal ($\\frac{1}{f(x)}$).","points":null},{"id":"95cf80e7-9e31-458b-a8b0-0c6e07a2e38d","cardType":"basic","front":"What is the inverse of $r(x) = 4x - 3$?","back":"$$r^{-1}(x) = \\frac{x+3}{4}$","points":2},{"id":"ca701d60-8a46-4a84-916e-53d8acd3b398","cardType":"basic","front":"In the composite function $gf(x)$, which function is applied to $x$ first?","back":"Function $f$ (the function nearest to $x$).","points":1},{"id":"7a974fef-578a-4ccb-9abe-6a82968c5545","cardType":"cloze","front":"Composite functions like $gf(x)$ are read from [ ].","back":"Composite functions like $gf(x)$ are read from right to left.","points":null},{"id":"1ec08c8f-1f5c-473f-9eb5-742132cbfbf7","cardType":"basic","front":"Why is $fg(x)$ not the same as $f(x) \\times g(x)$?","back":"Composite notation indicates a chain of operations, not multiplication of the two formulas.","points":1},{"id":"099cb1b0-07f0-47e3-8c05-366d7051bcb2","cardType":"basic","front":"Given $f(x) = 2x + 1$ and $g(x) = x^2$, calculate $fg(x)$.","back":"$$2x^2 + 1$","points":2},{"id":"2ecad63a-a488-4e8b-84bd-927a24c36528","cardType":"basic","front":"Given $f(x) = 2x + 1$ and $g(x) = x^2$, calculate $gf(x)$.","back":"$$(2x + 1)^2$","points":2},{"id":"0bdff87c-d879-4237-93fa-8c273921c7a4","cardType":"cloze","front":"When finding $f(x-3)$, you must substitute the [ ] $(x-3)$ wherever $x$ appears in the original function.","back":"When finding $f(x-3)$, you must

Inverse and Composite Functions Flashcards

Inverse and Composite Functions Flashcards

Inverse and Composite Functions Flashcards

Inverse and Composite Functions Flashcards