Sign up to access problem solutions.

Already have an account? Log in here.

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.

Let \( f(x) \) be a cubic polynomial such that \( f(1) = 5, f(2) = 20, f(3) = 45 \).

Then find the product of roots of the equation below.

\[ \large [f(x)]^{2} + 3x \ f(x) + 2x^{2} = 0 \]

Sign up to access problem solutions.

Already have an account? Log in here.

Let \(f\) be a function from the integers to the real numbers such that \[ f(x) = f(x-1) \cdot f(x+1). \]

What is the maximum number of distinct values of \(f(x)\)?

Sign up to access problem solutions.

Already have an account? Log in here.

Let \(f(x)\) be a polynomial. It is known that for all \(x\),

\[\large f(x)f(2x^2) = f(2x^3+x)\]

If \(f(0)=1\) and \(f(2)+f(3)=125\), find \(f(5)\).

Sign up to access problem solutions.

Already have an account? Log in here.

Sign up to access problem solutions.

Already have an account? Log in here.

The functions \(f(x)\) and \(g(x)\) are defined \(\mathbb {R^+ \to R}\) such that \[f(x)=\begin{cases} 1-\sqrt{x}\quad \text{x is rational} \\ \quad x^2\quad\quad\text{x is irrational}\end{cases}\\g(x)=\begin{cases} \quad x\quad\quad~~~ \text{x is rational} \\ 1-x\quad\quad\text{x is irrational}\end{cases}\]

The composite function \(f \circ g(x)\) is

Sign up to access problem solutions.

Already have an account? Log in here.

×

Problem Loading...

Note Loading...

Set Loading...