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Use the following function rule to find f(40)f(40).\newlinef(x)=1265−xf(x) = 12\sqrt{65 - x}\newlinef(40)=f(40) = _____

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Full solution

Q. Use the following function rule to find f(40)f(40).\newlinef(x)=1265−xf(x) = 12\sqrt{65 - x}\newlinef(40)=f(40) = _____
  1. Identify Function and Input: Identify the function and the input value.\newlineWe are given the function f(x)=1265−xf(x) = 12\sqrt{65 − x} and we need to find the value of f(40)f(40).
  2. Substitute Input into Function: Substitute the input value into the function.\newlineTo find f(40)f(40), we substitute xx with 4040 in the function:\newlinef(40)=1265−40f(40) = 12\sqrt{65 − 40}
  3. Perform Subtraction in Square Root: Perform the subtraction inside the square root.\newlineCalculate the value inside the square root:\newline65−40=2565 − 40 = 25
  4. Simplify Square Root: Simplify the square root.\newlineSince the square root of 2525 is 55, we have:\newline25=5\sqrt{25} = 5
  5. Multiply by Coefficient: Multiply the result by the coefficient.\newlineNow, multiply the square root by 1212 to find f(40)f(40):\newlinef(40)=12×5f(40) = 12 \times 5
  6. Calculate Final Result: Calculate the final result.\newlinePerform the multiplication to get the final answer:\newlinef(40)=60f(40) = 60

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