Algebra

Functions

Functions: Level 1 Challenges

         

If ab=(a+b)2 a \oplus b = \left( a+b \right) ^{ 2 } , what is the value of 31 3\oplus 1?

Consider a function ff satisfying f(x)=x37xf(x) = | x^{3} - 7x |. What is the value of f(3)f(3) ?

If ff is a function such that f(f(x))=x21 f(f(x)) = x^2 - 1 , what is the value of f(f(f(f(3)))) f(f(f(f(3)))) ?

Consider a function ff satisfying

f(x)=x2.f\big(\sqrt{x}\big)=x^2.

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

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

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