Flashcards · Maths · Functions, Sequences and Rates of Change
Functions and Function Notation
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What is a function?
A rule that gives exactly one output for each input.
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What does \(f(4)\) mean?
The output when the input is 4.
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How do you work out \(f(a)\)?
Replace \(x\) with \(a\) in the rule.
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What does \(fg(x)\) mean?
\(f(g(x))\), where \(g\) is applied first.
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Which function is applied first in \(gf(x)\)?
\(f\).
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Are \(fg(x)\) and \(gf(x)\) always equal?
No.
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What does \(ff(x)\) mean?
\(f(f(x))\), applying \(f\) twice.
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What is \(f^{-1}(x)\)?
The inverse function of \(f\).
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Is \(f^{-1}(x)\) the same as \(\dfrac{1}{f(x)}\)?
No, it is the inverse function, not a reciprocal.
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What are the steps to find an inverse?
Write \(y = f(x)\), make \(x\) the subject, then swap \(y\) and \(x\).
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What is the inverse of \(f(x) = x + 5\)?
\(f^{-1}(x) = x - 5\).
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What is the inverse of \(f(x) = 3x\)?
\(f^{-1}(x) = \dfrac{x}{3}\).
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What is \(f(f^{-1}(x))\)?
\(x\).
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If \(f(x) = 2x + 1\), what is \(f(3)\)?
7.
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How do you check an inverse?
Try a number through the function and then the inverse.
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Which tier are functions?
Higher tier on all boards.