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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 1

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

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

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

Consider a function $$f$$ satisfying

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

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

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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