Find and simplify each of the following for $f(x) = 6x^2 - 8x + 9$. (A) $f(x + h)$ (B) $f(x + h) - f(x)$ (C) $ \frac{f(x + h) - f(x)}{h}$ (A) $f(x + h) = $ (Do not factor.)
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To do this, we will substitute (x + h) into the function f(x) = 6x^2 + 8x + 9. f(x + h) = 6(x + h)^2 + 8(x + h) + 9 Now, we will expand and simplify the expression: f(x + h) = 6(x^2 + 2xh + h^2) + 8x + 8h + 9 f(x + h) = 6x^2 + 12xh + 6h^2 + 8x + 8h + 9 Show more…
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