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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.

Level 2

Consider a function \(f\) satisfying

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

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

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

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

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

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

Find the value of \(k\) such that

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

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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