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Functions map an input to an output. For example, the function f(x) = 2x takes an input, x, and multiplies it by two. An input of x = 2 gives you an output of 4. Learn all about functions.

If \( a \oplus b = \left( a+b \right) ^{ 2 } \) , what is the value of \( 3\oplus 1\)?

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Consider a function \(f\) satisfying \(f(x) = | x^{3} - 7x |\). What is the value of \(f(3) \)?

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If \(f\) is a function such that \( f(f(x)) = x^2 - 1 \), what is the value of \( f(f(f(f(3)))) \)?

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Consider a function \(f\) satisfying

\[f(\sqrt{x})=x^2.\]

What is the value of \(f(2) ? \)

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If \(f\left( x \right) =ax+b\), where \(a\) and \(b\) are real numbers, and \(f\left( f\left( f\left( x \right) \right) \right) =8x+21\), what is \(a+b\)?

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