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Use the following function rule to find f(2). f(x) = -6(12)^x - 7. f(2) = [input box]

Check the final answer first, then review the worked steps.

Problem

Use the following function rule to find f(2). f(x) = -6(12)^x - 7. f(2) = [input box]

Answer

\(-871\)

Step-by-step solution

  1. Identify the function rule: The given function rule is $f(x) = -6(12)^x - 7$.
  2. Determine the value to substitute for x: We need to find $f(2)$, which means we need to substitute $x=2$ into the function rule.
  3. Substitute x = 2 into the function: Replace every instance of $x$ in the function rule with $2$. This gives us $f(2) = -6(12)^2 - 7$.
  4. Calculate the exponent: First, calculate $12^2$. $12^2 = 12 imes 12 = 144$.
  5. Perform the multiplication: Now, substitute the value of $12^2$ back into the equation: $f(2) = -6(144) - 7$. Next, multiply $-6$ by $144$. $-6 imes 144 = -864$.
  6. Perform the subtraction: Finally, subtract $7$ from $-864$. $f(2) = -864 - 7 = -871$.