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# Functions

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.

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Consider a function \(f\) satisfying

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

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

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Aman Sharma**

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Suppose \(f\) is a real function satisfying \(f(x+f(x)) = 4f(x)\) and \(f(1)=4\). What is \(f(21)\)?

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Paul Ryan Longhas**

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Given that \(f(2^x)+xf(2^{-x})=1\), find the value of \(f(2)\).

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Nelson Mandela**

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\[x * y = \frac{1}{x} + \frac{1}{y}, \quad x \# y = \frac{x+y}{x-y}\]

Let the operations \(\#\) and \(*\) be defined as described above.

Find the value of \(k\) such that

\[(22 * k) \# (k * 33) = 27.\]

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Christian Daang**

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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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Júlian Rikki Réyes**

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