Sub-topic 1
2025 · National One-Eighth
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Domain of $f(x)=\sqrt{x^2+3}$
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Sub-topic 2
2025 · National One-Eighth
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Range of $y=\dfrac{4x+3}{3x+4}$
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Sub-topic 3
2025 · National One-Eighth
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Range of a rational function $y=\dfrac{ax+b}{cx+d}$ (second contest)
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Sub-topic 4
2024 · National Preliminary
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A function $f$ and its reciprocal $g(x)=\dfrac{1}{f(x)}$ (true/false)
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Sub-topic 5
2024 · National Preliminary
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Inverse of $f(x)=\dfrac{x-1}{x-2}$, $\dfrac{2x-1}{3x+2}$ and $\dfrac{x+1}{1-2x}$
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Sub-topic 6
2026 · National Preliminary
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Inverse of $y=\dfrac{3x-2}{2x+3}$
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Sub-topic 7
2025 · National Preliminary
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Inverse of $f(x)=\dfrac{3x+1}{2x+1}$
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Sub-topic 8
2023 · National Preliminary
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Inverse of $f(x)=\dfrac{2x+3}{x-5}$
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Sub-topic 9
2024 · National Preliminary
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Range of $y=\dfrac{2x-3}{x+2}$
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Sub-topic 10
2026 · National Preliminary
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Evaluating $g(f(2))$ for $f(x)=x^2-5$ and $g(x)=2x-3$
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Sub-topic 11
2018 · National Preliminary
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Evaluating $f(g(h(2)))$ for $f(x)=x^2+3$, $g(x)=2x+3$ and $h(x)=5-3x$
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Sub-topic 12
2018 · National Preliminary
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Finding $f(x)$ given $f(x+2)=x^2+4x+5$
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Sub-topic 13
2018 · National Preliminary
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Riddle: rational functions as a quotient of polynomials
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Sub-topic 14
2023 · National One-Eighth
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Even and odd functions such as $f(x)=x^2+2x$ (true/false)
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Sub-topic 15
2021 · National One-Eighth
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Composite function $f(g(x))$ for $f(x)=x^2+5$ and $g(x)=2x-3$
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Sub-topic 16
2024 · National One-Eighth
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Inverse of $f(x)=\dfrac{x+2}{x-3}$, $x\neq3$
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Sub-topic 17
2026 · National Preliminary
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Inverse of $y=\dfrac{x+1}{x}$
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Sub-topic 18
2023 · National Final
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Domain of $f(x)=\sqrt{18-3x-x^2}$
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Sub-topic 19
2026 · National Preliminary
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Composition of functions: associative, commutative, binary operation (true/false)
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Sub-topic 20
2023 · National Preliminary
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Finding $f(x)$ given $f(3x-2)=x^2$ and similar equations
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Sub-topic 21
2016 · National One-Eighth
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Is $f(x)=4x^2-5$ an even function? (true/false)
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Sub-topic 22
2016 · National One-Eighth
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Is $f(x)=3x^3-2x$ an odd function? (true/false)
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Sub-topic 23
2016 · National One-Eighth
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Is $f(x)=2x+1$ neither even nor odd? (true/false)
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Sub-topic 24
2016 · National One-Eighth
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Riddle: a constant function's horizontal graph with a single-element range
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Sub-topic 25
2017 · National Semifinal
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Domain of $f(x)=\dfrac{3}{\sqrt{x-5}}$
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Sub-topic 26
2017 · National Semifinal
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Domain of $f(x)=\sqrt{x^2-6x}$
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Sub-topic 27
2017 · National Semifinal
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Domain of $f(x)=\dfrac{\sqrt{x-2}}{x}$
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Sub-topic 28
2020 · National Preliminary
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Domain of $f(x)=x^2-3x+2$
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Sub-topic 29
2021 · National Preliminary
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Finding $f(x)$ given $f(x-2)=x^2-4x-1$
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Sub-topic 30
2022 · National Preliminary
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True or false: a many-to-many relation is a mapping (function)
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Sub-topic 31
2022 · National Preliminary
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True or false: a many-to-one relation is a mapping (function)
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Sub-topic 32
2022 · National Preliminary
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True or false: every mapping (function) is a one-to-one relation
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Sub-topic 33
2022 · National Preliminary
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Inverse of $y=\dfrac{2x+1}{x+2}$
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Sub-topic 34
2022 · National Preliminary
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Inverse of $y=\dfrac{x-2}{2x+3}$
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Sub-topic 35
2022 · National Preliminary
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Inverse of $y=\dfrac{2x+1}{x-1}$
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Sub-topic 36
2022 · National Preliminary
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Evaluating $f(-1)$ given $f(2x-3)=3x-5$
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Sub-topic 37
2022 · National Preliminary
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Evaluating $f(-4)$ given $f(3x+2)=2x+3$
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Sub-topic 38
2022 · National Preliminary
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Evaluating $f(-5)$ given $f(3-4x)=3x+5$
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Sub-topic 39
2023 · National Preliminary
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Finding $f(x)$ given $f\left(\dfrac{x+1}{2x-1}\right)=x$
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