Functions
Suppose that \[\begin{align} f(x) &=4x^2-9,\\ g(x) &=3x+7,\\ h(x) &=f(x)+g(x). \end{align}\] What is the value of \(h(3)\)?
Consider the functions \[\begin{align} f(x)&=-5x+7,\\ g(x)&=-2x-3. \end{align}\] What is the value of \(f(6) \cdot g(1)\)?
Given the two functions \[f(x) = 2x + 1, \quad g(x) = -x - 2,\] if \[h(x) = f(x) + g(x), \quad k(x) = f(x) - g(x),\] what is the value of \( h(2) \cdot k(1)? \)
Consider the functions \[ \begin{align} f(x) &= 3x + 1 \\ g(x) &= x + \frac{1}{3}. \end{align} \] If \[ \begin{align} h(x) &= f(x) + g(x) \\ k(x) &= \frac{g(x)}{f(x)}, \end{align} \] what is the value of \( x \) satisfying \( h(x) - k(x) = 5? \)
Suppose that \[\begin{align} f(x)&=-6x+7,\\ g(x)&=-3x-3. \end{align}\] What is the value of \(f(6) \cdot g(2)\)?