Function Arithmetic


Suppose that f(x)=4x29,g(x)=3x+7,h(x)=f(x)+g(x).\begin{aligned} f(x) &=4x^2-9,\\ g(x) &=3x+7,\\ h(x) &=f(x)+g(x). \end{aligned} What is the value of h(3)h(3)?

Consider the functions f(x)=5x+7,g(x)=2x3.\begin{aligned} f(x)&=-5x+7,\\ g(x)&=-2x-3. \end{aligned} What is the value of f(6)g(1)f(6) \cdot g(1)?

Given the two functions f(x)=2x+1,g(x)=x2,f(x) = 2x + 1, \quad g(x) = -x - 2, if h(x)=f(x)+g(x),k(x)=f(x)g(x),h(x) = f(x) + g(x), \quad k(x) = f(x) - g(x), what is the value of h(2)k(1)? h(2) \cdot k(1)?

Consider the functions f(x)=3x+1g(x)=x+13. \begin{aligned} f(x) &= 3x + 1 \\ g(x) &= x + \frac{1}{3}. \end{aligned} If h(x)=f(x)+g(x)k(x)=g(x)f(x), \begin{aligned} h(x) &= f(x) + g(x) \\ k(x) &= \frac{g(x)}{f(x)}, \end{aligned} what is the value of x x satisfying h(x)k(x)=5? h(x) - k(x) = 5?

Suppose that f(x)=6x+7,g(x)=3x3.\begin{aligned} f(x)&=-6x+7,\\ g(x)&=-3x-3. \end{aligned} What is the value of f(6)g(2)f(6) \cdot g(2)?


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