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Use the following function rule to find f(2). f(x) = -11(4)^x

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

Problem

Use the following function rule to find f(2). f(x) = -11(4)^x

Answer

\(-176\)

Step-by-step solution

  1. Identify the function rule: The given function rule is $f(x) = -11(4)^x$.
  2. Determine the value to substitute for x: We need to find $f(2)$, so we will substitute $x=2$ into the function rule.
  3. Substitute the value of x into the function: Replace every instance of $x$ in the function rule with $2$: $f(2) = -11(4)^2$.
  4. Calculate the exponent: Evaluate $4^2$. $4^2 = 4 \times 4 = 16$.
  5. Perform the multiplication: Multiply $-11$ by the result from the previous step: $f(2) = -11 \times 16$.
  6. State the final result: $f(2) = -176$.