Algebra

# Function Arithmetic

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 $$f(6) \cdot g(2)$$?

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