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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.

Given two functions:

\(f(x)=x+3\)

\(g(x)=\dfrac{x}{2}\)

Find the value of \(g(f(5))\).

For the two functions \[f(x)=x^2+5x, \, g(x)=x+22,\] what is the value of \((g \circ f)(9)?\)

**Details and assumptions**

\( (g \circ f)(x) \) is the composition of \(g\) and \(f\), defined by \((g \circ f)(x)= g(f(x))\).

Let \(f\) be a function such that \((f \circ f)(x) = x^2\)

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

Consider the two functions \[f(x)=6x-5, g(x)=\begin{cases} -x+4 & \text{ if } x \geq 1, \\ 17 & \text{ if } x<1. \end{cases}\] What is the value of \((f \circ g)(2)+(g \circ f)(0)\)?

**Details and assumptions**

\( (g \circ f)(x) \) is the composition of \(g\) and \(f\), defined by \((g \circ f)(x)= g(f(x))\).

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