Functional Equations
If \(f\) is a function satisfying \(f(x+y) = 3^yf(x)+2^xf(y)\) for all \(x,y \in R\) and \(f(1) = 1\), what is the value of \(f(3)\)?
by
Ishan Tarunesh
The polynomial function \( f: \mathbb{R}^+ \rightarrow \mathbb{R}^+\) satisfies the functional equation
\[ f(f(x) ) = 6x + f(x). \]
What is the value of \( f(17) \)?
by
Sanjeet Raria
A function \(f: \mathbb{R} \rightarrow \mathbb{R}\) satisfies \( f (5-x) = f(5+x) \). If \(f(x) = 0 \) has \(5\) distinct real roots, what is the sum of all of the distinct real roots?
Details and assumptions
The root of a function is a value \( x^*\) such that \( f(x^*) =0\).
by
Calvin Lin
Let a function \(f(x)\) has the property:
\[ f(x+2)= \frac{ f(x)-5}{f(x)-3}. \]
Then, which of the following must be equal to \( f(2014) \)?
by
Sanjeet Raria
Let \(f : \mathbb R^+ \rightarrow \mathbb R \) such that \[f(x)+2f \left (\frac{1331}{x} \right )=L \cdot x \] where \(L\) is a constant.
Knowing that \(f(11)=847\), what is \(L \)?
by
Sanjeet Raria